
69 N.W.2d 920 (1955)
160 Neb. 250
Betty Lee HENNEBERG and Carrol G. Henneberg, Appellants,
v.
COUNTY OF BURT, Nebraska, etc., Appellees.
No. 33670.
Supreme Court of Nebraska.
April 22, 1955.
*921 Richards, Yost & Schafersman, Fremont, Keith Hopewell, Tekamah, for appellants.
Paul W. Eagleton, Fred S. Jack, Ralph M. Anderson, Ellenberger & Pipher, Tekamah, for appellees.
Heard before SIMMONS, C. J., and CARTER, MESSMORE, YEAGER, CHAPPELL, WENKE and BOSLAUGH, JJ.
BOSLAUGH, Justice.
Appellants have been since March 1949 the owners of the southwest quarter and the south half of the northwest quarter of Section 5, and the southeast quarter of the northeast quarter of Section 6, Township 22 North, Range 11 East, of the 6th P. M. in Burt County. This land is within the Burt-Washington Drainage District, hereinafter called the district, and the land has been assessed for benefits. The works designed and constructed by it were completed and put in operation about the year 1916. The district located and excavated a ditch along the center line of Section 5 from the north to and beyond the south line of Section 5. The ditch was along the east boundary of the land of appellants. It was known as the Litel ditch. It is designated herein as the ditch. Its specifications were bottom width 4 feet, depth 6.1 feet, side slopes 1 foot horizontal to 1 foot vertical, and the top width was about 16 feet. There was a public highway along the south of the land of appellants. The district designed and constructed a bridge at the location where the ditch intersected the highway. It was 16 feet long and 16 feet wide. The manner of its construction was that holes were bored in *922 the banks of the ditch and concrete was placed in the holes. The concrete therein was used as piling. About 3 feet of wall piers or bridge caps were built on and above the concrete piling. Metal I-beams were laid lengthwise on the bridge caps and wood planks were placed transversely on the I-beams for the deck or floor of the bridge.
The bridge was maintained by the County of Burt, identified as the county herein, until the Missouri River flood in April 1952, washed away the support of the bridge at its east end. The bridge cap toppled over and the floor or deck of the bridge at that end fell downward into the ditch. The west end of the bridge and its floor were otherwise undamaged. In May 1952 the county removed what remained of the bridge and substituted a tube 60 inches in diameter. This was the means for the passage of water flowing in the ditch to cross the highway near the southeast corner of the land of appellants until it was removed in November of that year. The county November 6, 1952, removed the tube from the highway described above and installed in lieu thereof a corrugated tube 72 inches in diameter and 34 feet in length. The installation of it and the incidental work necessary to put the highway in suitable condition for travel were completed the following day. The first tube was placed in the ditch so the lowest part of it was 1 foot above the grade of the ditch. It was decided by the county that was not proper engineering. The second tube had 1 foot greater diameter and greater capacity. The lower part of it at the inlet was on the grade of the ditch with a decline of about forty-five hundredths of a foot at the outlet of it.
This litigation concerns the effect of the substitution by the county of the metal tube with a diameter of 72 inches for the bridge constructed by the district. Appellants assert that the latter was adequate and allowed all water in the ditch to flow to the south from the land of appellants without damage to it; that the size of the tube is much smaller than that of the ditch; that it is insufficient to permit the water to flow to the south; and that it acts as an obstruction and causes the water to build up in the ditch and overflow onto the land of appellants to their damage present and prospective. The relief appellants seek is a mandatory injunction requiring appellees to construct an opening across the road of the capacity and condition as it was before the original bridge was removed, and to erect at the location of the metal tube a bridge of the same character and condition as the one that existed at that location at the time the bridge was damaged by the flood in 1952.
The position of the county was that the bridge across the ditch near the southeast corner of the land of appellants was washed away by the flood of 1952; that the county upon the recommendation and approval of the district placed a 60-inch steel tube 34 feet in length in the ditch through the highway; that it adequately carried the flow of water in the ditch; that it was removed because it was positioned higher than the bottom of the ditch and the county about the time of the filing of this case replaced it with a 72-inch steel tube 34 feet in length through the highway in a proper position to accommodate the flow of water to the capacity of the ditch; that the tube is an adequate structure for the flow of the water in and is a suitable bridge across the ditch; and that appellants have not and will not suffer any damage because of the change made in the structure in that location.
The township responded to the claims of appellants that it had nothing to do with and took no part in the removal of the bridge identified in their petition or in the installation of the culvert substituted for the bridge.
The district traversed the allegations of appellants and asserted that it had no part in the removal of the bridge or the installation of the steel tubing; that the change was made in that respect solely by the county which was responsible for the maintenance of the bridge; that the 60-inch metal tube substituted by the county for the bridge was not placed to the proper grade in the ditch, and the county removed and replaced it with a 72-inch steel tube November *923 6, 1952; that it is a good and sufficient bridge over the ditch, and does not and will not constitute an obstruction of the ditch or restrict or reduce the drainage capacity thereof; and that any flooding of the lands of appellants would have occurred in any event and was not due to the installation of the steel tube.
The result of the trial was a finding for appellees and against appellants and a judgment of dismissal.
The allegations made by appellants concerning the town of Riverside were that it was a township in Burt County; that it consented to the removal by the county of the bridge constructed by the district across the ditch at its intersection with the highway south of the land of appellants and the substitution of a 60-inch steel culvert for the bridge; that it was the duty of the township to maintain the bridge; and that the negligent and wrongful acts of the township, not otherwise specified, caused the water in the ditch to and it did flow upon the lands of appellants during the summer of 1952. The admissions and proof concerning the town of Riverside were that it was a township of the county; that the road referred to above is a township road; and that the township had a road maintainer and that it maintained the road. It is established in the record that the district built the bridge and that the county maintained it until it was damaged in 1952. There is nothing to establish that the township had anything to do with or concerning the bridge, its removal, or the installation of either of the metal tubes in the highway. It definitely does not appear that the township had any opportunity to consent or that it did consent to the elimination of the bridge or the substitution of a metal tube for it. There is a failure of proof that the township had any knowledge of or participation in the changes that were made in this regard.
The road involved was a public road. A road established by law, opened by the county board of any county, and traveled for more than 10 years is a public road. Section 39-101, R.R.S.1943. The county board has general supervision over the roads of the county and is obligated to respect and execute the laws in relation to them except to the extent that the state has undertaken the construction and maintenance of any highway in the county. Sections 39-103, 39-604, R.R.S.1943; State ex rel. Johnson v. County of Gage, 154 Neb. 822, 49 N.W.2d 672; Porter v. Lancaster County, 130 Neb. 705, 266 N.W. 584; Cheney v. County Board of Supervisors, 123 Neb. 624, 243 N.W. 881.
The district had, in the absence of an agreement with the county, the responsibility to construct a proper bridge across the ditch where it intersected the highway and the county was obligated to maintain it. Section 2983, R.S.1913; Section 39-805, R.R.S.1943; State ex rel. County of Burt v. Burt-Washington Drainage Dist., 103 Neb. 763, 174 N.W. 316; Ritter v. Drainage District No. 1, 148 Neb. 873, 29 N.W.2d 782. It is not claimed or established that there was an agreement between the county and the district concerning the construction and maintenance of the bridge. The county recognized its responsibility and attempted to discharge it. It cannot escape the effect of any default on its part in this regard. Franek v. Butler County, 127 Neb. 852, 257 N.W. 235. The dismissal of the cause as to the township was correct.
The allegations made by appellants in reference to the district were that it was an organized and existing district by virtue of the laws of the state; that it constructed the bridge that was partially destroyed by flood in 1952; that it was its duty to maintain the bridge; that it was removed after it was damaged by the county with the consent of the district; that the county replaced the bridge with a 60-inch steel culvert which was insufficient to allow the water in the ditch in which it was placed to flow south from the lands of appellants; that the culvert caused the water to build up in the ditch and flow onto the property of appellants to their damage; that it would continue to do so in the future; and that because of the wrongful and negligent acts of the district, not otherwise stated, the *924 ditch overflowed during the summer of 1952 upon the lands of appellants.
The essence of the charge made by appellants against the district is that it consented to the removal of the bridge and the installation by the county of the metal tube at the location where the bridge had been since the works of the district were constructed until it was damaged in 1952. There was no allegation of any other act or omission of the district. There is no competent evidence of any authorized or binding act or statement of the district concerning the removal of the bridge or the installation of either of the metal culverts. The bridge was designed and constructed by the district. There is no claim or proof of any agreement of the county and district concerning the construction and maintenance of the bridge. It was the sole duty and right of the county to supervise and maintain the bridge. Section 2983, R.S. 1913; Section 39-805, R.R.S.1943; State ex rel. County of Burt v. Burt-Washington Drainage Dist., supra; Ritter v. Drainage District No. 1, supra. The county only was obliged to solve the difficulty that resulted from the damage to the bridge. The district had no right or authority to do anything in reference to it and the proof does not show that it attempted to exercise any influence or authority concerning what should be or was done by the county to solve the problem. The record justifies the dismissal of the case as to the district.
The disposition of this case requires a decision of whether or not the 72-inch steel tube installed in the ditch by the county at the place formerly occupied by the bridge has sufficient capacity for the unobstructed and unimpeded passage of the waters which it may reasonably be expected the ditch will bring to the intake of the tube. The opening under the bridge provided by the district was, according to the evidence, adequate to and it did satisfactorily perform that function for more than 35 years. The county could not legally abandon the bridge and insert in the ditch a structure or facility in replacement of the bridge that would do less, to the injury and damage of property owners affected adversely by the change.
The testimony of an engineer offered by appellants is in substance that he measured the ditch at a point 45 feet north of the north end of the 72-inch steel tube the day before he testified in the case, and that he inspected the ditch and while there were some variations in its size it was generally, as far as could be determined from observing it, quite uniform. His measurements were and he testified that the ditch was at its bottom 11 feet in width; that it was 8 feet deep; that its width at the top was 32 feet; that the cross-section area of the ditch was 172 square feet; that the 72-inch metal tube had a cross-section area of 28 square feet; and that it was his judgment and opinion that the tube was thoroughly inadequate to accommodate the flow of water to the capacity of the ditch. The conclusion of the witness was deduced from and based upon a comparison of the area of the opening of the tube reduced to square feet with the cross-section area of the ditch expressed in square feet. He excluded all other facts such as speed and momentum of the water, the manner in which the tube was installed, and the decline of the pipe from the inlet downward to its outlet, and other similar considerations. He testified that the result of a ditch with a greater capacity than an opening through which water in the ditch must pass is that the enclosure around the opening acts as a dam, obstructs the flow of the water, and causes it to build up in the ditch. The effect of the testimony of the witness was considerably dissipated by his extravagant opinion that a tube to carry water to the capacity of the ditch should be 20 feet in diameter, his unusual activities on behalf of appellants, and his unconcealed desire that their case succeed. These were obviously as great as if he had been the party plaintiff in the case.
An engineer presented as a witness by appellants considered that the surface water from 735 acres of land drained into the ditch south of a concrete culvert about a mile north of the 72-inch tube involved in *925 this inquiry. He said that engineers used one of several formulas to determine the proper size of the opening under a bridge or of a culvert in a given situation, and that the one generally in use in this territory is Talbot's formula. There are two factors in the formula, the coefficient of the area and the drainage area. The witness accepted from the formula the equation that A = .3. He interpreted it to mean ".3 times the square root of the area squared, raised to the fourth power." He applied this to the drainage area of 735 acres, did the necessary arithmetic, and arrived at the conclusion that the area of a cross section of the opening of any structure placed in the ditch at the location in question sufficient to permit the passage of water to the capacity of the ditch must be 42.35 square feet. He said the area of a cross section of the tube was 28 square feet. He expressed the opinion that the 72-inch tube was inadequate to perform the function intended of it.
A third engineer deposed as an expert at the instance of appellants that engineers generally compute the size of a bridge or culvert opening by the use of a formula and for this purpose he considered the Talbot formula as the one generally employed. He used this and on the basis of his estimate that the drainage area was 1,920 acres of land he found and testified that the size of the opening of a structure sufficient to carry the water across the road involved in this case was 60 square feet. He computed the area of the opening of the 72-inch tube as 28.3 square feet. He concluded that the tube was inadequate to permit an unobstructed flow of the water which the ditch may be expected to drain to the inlet of the tube.
An engineer was presented by the county who testified that the size of the ditch 45 feet north of the inlet of the tube where the first engineer who testified for appellants made his measurements of the ditch was very much larger than the average size of the ditch; that the average cross-sectional capacity of the ditch at the time of the trial measuring 6 feet upward from the bottom of the ditch was 97 square feet; that the discharge capacity of the ditch at 6 feet deep was 317½ cubic feet per second; that the discharge capacity of the 72-inch tube was 230 cubic feet per second; that the maximum discharge or run-off from the drainage area was 230½ cubic feet per second; that he used the depth of 6 feet because water that deep in the ditch would be up to about the original bank line and it would then begin to back up and go through the various openings from the ditch into the fields and into the road ditches; that if water was 6 feet deep in the ditch it would be up to the top of the tube and if it was 7 feet deep it would overflow the land of appellants; and that the cross-sectional area of the opening under the bridge as it was before the bridge was damaged was not less than 40 square feet and was not more than 50 square feet.
The engineer who designed and supervised the construction of the works of the district was a witness called by the county. He said the drainage area of the district was 1,500 acres. The discharge capacity of the original ditch was 125 cubic feet per second. The discharge capacity of the ditch at the time of the trial when filled with water to the depth of 6 feet was 187½ cubic feet per second. The maximum run-off to be reasonably expected from the drainage area was 125 cubic feet per second. The tube has a discharge capacity of 230 cubic feet per second, a difference of 105 cubic feet per second in favor of the tube and this is an abundant safety factor. A comparison of a cross section of the ditch with a cross-section area of the tube is not a fair or true test of the efficiency or service-ability or discharge capacity of the tube. This method of comparison is an unsound test of the capacity of the tube. "As far as efficiency (of the tube) is concerned it is comparing the velocity of a two-plus against seven. You have a velocity of two, and say this formed a velocity of seven feet per second. If the velocity were much higher then it would be even greater difference. That affects you on comparison of areas. We have to take the area and the velocity both to get a fair comparison." The tube was installed *926 properly in compliance with approved engineering practices. There was a fourtenths of a foot decline of the tube from its inlet to its outlet and the ditch at the location of the tube had a downward grade to the south. These facts resulted in water passing through the tube developing maximum velocity. The witness explained in this way how the tube functioned: "A tube carrying water under normal conditions has its maximum velocity when it is half-full; also when it is running full, and it operates to carry water as in this case and under similar conditions, by developing a velocity that would run up to say seven feet a second, which is the mean velocity in the Missouri River, bank full * * *. It has a lot of * * * open space, when it is running half-full and gets a maximum efficiency as far as velocity is concerned under those conditions. The velocity is greater than it would be in the ditch approaching or in the ditch leaving the location of the pipe." The witness said the tube would not obstruct, hold back, or back up the water in the ditch. The tube does not require the build-up of a head of water to make it perform its function. The ditch by virtue of its situation is in itself a head. The opinion of the witness was the tube was ample to discharge all water brought to it by the ditch. He explained his opinion in this language: "My opinion is that the seventy-two inch culvert will never back the water out onto any of the drainage area; that it will never run full so that there would be no head on the pipe, for the reason that if you had a two-inch rate of run-off, which I think is ample under existing conditions it would take a little more than half the capacity of the pipe to provide that much discharge capacity and still you would have daylight and room for trash. There wouldn't be any back-water."
The evidence is irreconcilably conflicting on the issue of the capability and suitability of the tube to promptly, without causing an overflow of adjacent land, discharge the water brought to its inlet by the ditch. The trial is de novo and the manner of it has been often stated. Keim v. Downing, 157 Neb. 481, 59 N.W.2d 602.
There are two significant and convincing facts. It is established without dispute that when the works of the district were designed the plans and specifications required a bridge 16 feet long across the ditch at the present location of the tube, notwithstanding that tubes were provided at that time in other parts of the district; that the bridge was constructed and maintained at that location for more than 35 years; and that the opening under the bridge was sufficient during that time to and it did according to the proof discharge all the water transported to it by the ditch without overflow or injury to any adjacent property. There has not been precipitation or run-off from the drainage area since the 72inch tube was installed in November 1952, to test or demonstrate its sufficiency or inadequacy to discharge the water the ditch is capable of bringing to the tube. However in June 1952 after the 60-inch tube was inserted in the ditch there was a rain of considerable intensity, the exact amount not being definitely shown in the record. The run-off caused thereby was sufficient to build up water at the intake of the tube at least 12 inches above the top of the opening in it, and the water backed up and overflowed onto and flooded about 120 acres of the land of appellants. Water was draining from the land of appellants as much as 2 or 3 days after the rain.
It is concluded that the 72-inch tube does not constitute an adequate or suitable opening to discharge the water that can be reasonably expected to be brought to it by the ditch in which the tube is installed at the place where the bridge was until it was damaged in 1952. It is the duty of one who places a structure or facility in a drainway to provide sufficient passage for all water which may reasonably be anticipated to be transported to the structure or facility by the drainway. In Schmutte v. State, 147 Neb. 193, 22 N.W.2d 691, 692, it is said: "Failure to make proper provision for the flow of water under a *927 bridge or culvert imposes liability, although such bridge or culvert may be constructed according to approved principles of engineering. The fact that it materially obstructs the flow is evidence that it was not properly constructed, regardless of the principles upon which it was built." See, also, Mader v. Mettenbrink, 159 Neb. 118, 65 N. W.2d 334. If an obstruction in a drainway is and will be a continuing and permanent injury to the lands of another he may on proper showing have a mandatory injunction for the removal of the obstruction and a restoration of the conditions existing before the advent of the obstruction. Andersen v. Town of Maple, 151 Neb. 103, 36 N.W.2d 620; Mader v. Mettenbrink, supra.
The judgment should be and is affirmed as to the appellees Town of Riverside and Burt-Washington Drainage District. The judgment should be and is reversed as to appellee County of Burt and the cause is remanded to the district court for Burt County with directions to render and enter a judgment granting appellants a mandatory injunction requiring the County of Burt with reasonable promptness, the circumstances considered, to remove from the highway south of the southwest quarter of Section 5, Township 22 North, Range 11, East of the 6th P.M. at the place where the drainage ditch of the Burt-Washington Drainage District intersects the highway, the 72-inch steel tube installed at that location by the county in the ditch aforesaid in November 1952, and to construct at that place a bridge comparable to the kind, size, and condition and with an opening beneath it for the discharge of water brought there by the ditch as existed in 1952 before the bridge then located there was damaged and removed.
Affirmed in part, and in part reversed and remanded with directions.
