In this article we will discuss about how to design cross drainage works.

**Design of cross drainage work includes the design of following elements: **

1. Determination of maximum flood discharge.

2. Determination of water way of the drain.

3. Contraction of canal water way if canal is to be flumed.

4. Head loss through syphon barrels.

5. Determination of uplift pressure on the bed of canal of drain whichever is above.

6. Determination of uplift pressure on the bed of canal or drain whichever is below.

7. Design of bank connections.

Besides the design of these elements, structural design of foundation, piers, abutment, syphon barrels, etc. also have to be done.

After having found out the above said hydraulic elements, the structural elements can be easily designed.

**1. Determination of Water Way of the Drain: **

After having decided about the maximum flood discharge, water way for the drain can be easily fixed by following Lacey’s equation-

P = 4.75 √Q …. (25.1)

For large drains, the perimeter (P) may be assumed equal to the width of the river. A contraction upto 20% of water way may be allowed in case of small drains. In large drains, no extra provision is made for the area covered by the piers.

While fixing the water way, it should ensure that a minimum velocity of flow from 2 to 3 m/sec may be maintained.

**2. Contraction of Canal Water Way: **

Contraction of canal is required only where type III aqueduct is to be installed. Fluming of the canal requires the provision of extra transition wings for joining the flumed portion to the normal section.

**While fluming the canal following points should be taken care of: **

(i) The velocity of flow through the flumed section of the canal is not more than 3 m/sec.

(ii) The flow should remain sub-critical without any formation of hydraulic jump.

(iii) The approach transition wings should not be steeper than 30° (splay of 2 :1) and departure transition should not be steeper than 22 ½° (splay of 3:1). See Fig. 25.8.

(iv) The transitions are curved and flared so that there is minimum loss of head and the flow is streamlined.

**The transitions can be designed for following two conditions: **

(a) Depth of water remains constant.

(b) Depth of water varies.

**(a) Depth of Water Remains Constant: **

For this design, following two formula may be used.

(i) R.S. Chaturvedis’s semi-cubical parabolic transition-

The values of x can be found out by choosing various convenient values of B_{x}.

(ii) AC Mitra’s hyperbolic transition-

The value of B_{x} can be found out by choosing various values of x.

In both the formulae, (Chaturvedis’s and Mitras)

B_{0} = normal width of the canal

B_{f} = Flumed width of the canal

B_{x} = Width at any distance x from the flumed section.

L_{f} = Total length of transition.

**(b) Depth of Water Varies: **

When depth of water varies, the design of transition is done by Hind’s method.

Consider Fig. 25.8. Let A-A and B – B be the sections of canal on the entrance side and C – C and D-D on the exit side. A – A and D-D are the normal sections of the canal and B – B and C – C are the limed sections of the canal.

Let D_{A}, D_{B}, D_{c} and D_{D} are the depths and V_{a}, V_{h}, V_{c}, V_{d}, the corresponding velocities of flow at sections A – A, B – B, C – C, and D-D respecting. See Fig. 25.8.

Design is started from the D/S side i.e., from section D-D.

1. Let bed level and cross-section of the canal at section D-D is completely known.

2. Loss of energy in expansion from section C – C to D – D is taken-

0.3 [(V^{2}_{c }– V^{2}_{d }/2g)]

3. The flumed channel section between B -B and C-C remains constant and no loss, other than friction occurs in it which can be worked out using Manning’s formula-

Since velocity and depth are constant in the flumed portion, T.E.L, level of water surface and level of bed are parallel to each other between sections B – B and C-C.

4. Loss of energy of head between section B – B and A – A due to contraction is taken 0.2 (V^{2}_{b }– V^{2}_{a }/2g)

Neglect friction losses.

5. Now bed level, water surface level and T.E.L. for all the four sections are known. The T.E.L. may be drawn straight between adjacent sections. The bed levels are also joined by straight line. If there is any fall it is provided either by rounding off the corners or with smooth reverse curve tangential to the bed. Smooth reverse curve is provided where drop in the bed levels is appreciable.

**Drop in water surface line depends upon following two aspects: **

(i) Increased velocity head for contraction and decreased velocity head for expansion.

(ii) Fall in T.E.L. between two adjacent sections.

This drop is accomplished by drawing two parabolas opposite to each other and meeting at mid drop points tangentially. Equation for parabola is-

Where y = ordinate at any distance x measured from the origin. Origin point of first parabola is section A – A and of second parabola section B – B.

X_{1} = L_{f} / 2 and y_{1} = half of the Total difference in water levels between A- A and B-B.

6. After having plotted the water profile over the full length of the flumed canal, the velocity head (h_{a}) at any point can be found, by determining difference between T.E.L. and corresponding water surface level at that point. The velocity head can be converted into equivalent velocity by formula-

Value of side slope can be interpolated in proportion to the length of transition from the starting point of the slope. Now A, D and S are known and Value of B can be computed at any point by substituting these values is equation A = BD + SD^{2}. Thus all the elements of transition are fully known.

**3. Head Loss through Syphon: **

**In case of syphon aqueduct and canal syphon, the head loss (h) is found out by unvin’s formula given below: **

Where, f_{1} = Coefficient of head loss at entrance whose value is taken 0.505 for unshaped mouth and 0.08 for bell mouth.

V_{a} = Velocity of approach.

V = Velocity of flow in m/sec.

R = H.M.D. of barrel.

L = Length of barrel in metres.

**Values of a and b for different materials are given as follows: **

The velocity of flow through syphon aqueduct is limited between 2 m to 3 m/sec. Knowing the velocity, the head required to generate the same, can be found out from Eq. 25.4. H.F.L. on the D/S side remains unchanged but H.F.L. on the U/S increases by the amount of afflux calculated by Eq. 25.4. The height of guide banks and marginal bonds is governed by the height of afflux.

**4. Determination of Uplift Pressure on Bed of the Canal or Drain Whichever is above: **

Once the afflux is found by Unwin’s formula, the hydraulic gradient line can be drawn and uplift pressure at various points determined. Uplift pressure will be proportional to the height of hydraulic gradient line above the underside of the trough. The maximum uplift pressure will be at the U/S point near the entry point and minimum at the D/S point near the exit.

**The trough is designed for the following two conditions: **

(i) There is H.F.L. in the drain but no water in the canal.

(ii) Canal running full but there is no uplift pressure.

**5. Uplift Pressure on Bed of the Canal or Drain Whichever Lies at the Lower Level: **

The most critical condition for the uplift at the bottom of the drainage (lying below) occurs when there is no flow in drainage and canal is running at full supply level. In case of siphon aqueduct if the floor is depressed below the water table then most critical condition is considered when underground water Table has risen to drainage bed and there is no water in drainage but canal is running at F.S.L.

In order to find out the head causing seepage at point C at the D/S end of impervious floor of drainage, the seepage water is assumed as starting from point A, the U/S end point of the impervious floor of the canal. Seeping water is considered to follow the path ABC. Total length of creep path (L) is sum of length from A to B i.e. (L_{1}) and B to C (L_{2}). Total head causing seepage (H_{s}) is as follows. See Fig. 25.10.

**H _{s} = F.S.L. of canal – D/S bed level of the drain Residual head (H_{r}) at point B is given as follows: **

The floor is finally designed for total uplift pressure which is sum of uplift pressure due seepage head and static head. The Total uplift pressure is resisted partly by weight of floor and partly by the bending action.

**The intensity of uplift pressure can be reduced by following measures: **

(i) Extend the impervious length of the canal bed U/S. This would increase the seepage length L_{1}.

(ii) By providing drainage holes in the floor of the drainage. To avoid the flow of soil through the drainage holes inverted filter is provided below them.

**6. Design of Bank Connections: **

The canal wings and drainage wings come under the category of Bank connections.

**Drainage Wings: **

They have to retain earth slope at their back. Their foundation should be deeper than the scour depth,

which is taken as 2R. Entry and exit should be smooth. The length of the drainage wings should be large enough to accommodate the splay in the drainage transition.

**Canal Wings: **

They are usually extended upto the end of the splay. In order to provide easy transition from channel section to aqueduct side walls, they are sometimes warped. They should be designed as retaining walls. They should be taken deep into the soil to avoid any short cut by seeping water.