# Energy dissipation below spillways

# ENERGY DISSIPATION BELOW SPILLWAYS

- When stream of water moving with hyper-critical velocity, meets an other stream, moving with sub-critical velocity there is abrupt rise in the water level of the stream.
- This abrupt rise of water is know hydraulic jump.
- Hydraulic jump is a very useful measure of dissipating the energy of flowing water.
- Flood water at the level of the crest of the spillway has potential energy proportionate to the rise of the crest above the D/S floor of the spillway.
- When flood water passing over the crest of spillway reaches the bottom of spillway on D/S side, the potential energy of water is convert into kinetic energy, as velocity is greatly increase by the time water reaches from crest to D/S floor of the spillway.
- This high kinetic energy may cause very deep erosions on D/S if measures to disscipate it are not taken.
- There are several methods of dissipating the energy of the shooting flow of water.

**The following are the most important measures: **

- Formation of hydraulic jump.
- Developing water cushion on D/S side.
- Stilling basins with or without blocks of different sizes and shapes arranged in different manners.
- Bucket type energy dissipators.
- Where excess energy of gliding water is to be dissipate before the flow joins the D/S main river channel, the hydraulic jump is considere one of the most effective measures.
- If spillway discharge is directly being spille into the river on D/S side, water cushion and other measures are considered best.

** Hydraulic Jump Computations. **

- The hydraulic jump that is forme at the stilling basin has some distinctive characteristics.
- The jump assumes a definite form depending upon the energy of flow to be dissipate in relation to the depth of flow.
- The form of jump depends upon the following factors:

(i) Discharge passing over the crest per metre length of the spillway (g),

(ii) Critical depth of flow (de), and

(iii) Froude number parameter which is V gd, various elements of the jump.

The depth of water jump can be compute as follows.

(a) For a given discharge q per metre length of the spillway, find out the total head of water (He) at the crest of the spillway including head due to velocity of approach.

\[H_{e}= \left ( \frac{g}{c}^{} \right)^{2/3}\]

U/S total energy line (T.E.L.) = crest level + He. If we consider that no loss of energy has taken place while transition from crest to toe, the specific energy (E1) at toe of the spillway will be equal to the T.E.L. at U/S.

\[E_{1}= U/S,T.E.L\]

After having found out E1 and q the depth (d1) of water at pre-jump position can be found by trial and error method.

\[E_{1}= d_{1}+\frac{V^{2}_{1}}{2g}= d_{1}+\frac{q^{2}}{2gd_{1}^{2}}\]

Determine Froude number F1

\[F_{1}= \frac{V_{1}}{\sqrt{gd_{1}}}= \frac{q}{\sqrt{gd_{1}^{3}}}\]

The depth of water at post jump (d2) can be found out from following equations

\[d_{2}= -\frac{d_{1}}{2}+\sqrt{\frac{2V_{1}^{2}d_{1}}{g}+\frac{d_{1}^{2}}{4}}\]

**or**

\[d_{2}= -\frac{d_{1}}{2}\left [ \sqrt{1+\frac{8q^{2}}{gd_{1}^{3}}}-1 \right ]\]

The values d2 can be plotted for various values of q and a curve known as jump height curve (J.H.C.) is plotted as shown in Fig. 14.12 (b).

The height of the tail water for each discharge, may or may not correspond to the height of perfect jump.

A curve relating depth of tail water (D) with discharge (q) may be drawn.

Such curves are known as tail water curves (T.W.C.). By comparing J.H.C. and T.W.C.

following five conditions of jumps are possible.

1. Both the curves coincide.

2. T.W.C. curve lies above the J.H.C. for all the discharges.

3. T.W.C. lies below the J.H.C. for all the discharges.

4. T.W.C. lies above for small discharges and then below at higher discharge.

5. Reverse of case 4.

**Case I**. Both the curves (J.H.C. and T.W.C.) coincide for all the discharges.

- The jump will be formed at the toe of the spillway.
- The post jump depth will be already available in the channel.
- The jump formation will be perfect for all the discharges.
- This condition requires horizontal apron of length 5(d2 – d1) beyond toe. See Figs 14.12 and 14.16 (d).

** Case II.**

- T.W.C. curve lies above the J.H.C. for all the discharges.
- In this case the value of jump height (d2) is less than the tail water depth.
- In this case jump will be completely submerged.
- In this case very little energy will be dissipated.
- But this condition can be made effective by reducing the depth of tail water at the point of formation of the jump. See Figs. 14.13, 14.14, 14.15 and 14.16 (b).
- The protection works in this case may be in the form of:

(i) A sloping apron instead of horizontal apron. See Fig. 14.13.

(ii) Using a low level bucket which is sharply turned up. It acts as a deflector. See Fig. 14.14.

(iii) Providing end sills with baffles. In this case energy is dissipated by impact and friction. See Fig. 14.15.

**Case III.**

- T.W.C. lies below the J.H.C. for all the discharges.
- In this case depth of tail water level is smaller than the depth of the jump for all the discharges.
- The protection of the bottom can be accomplished by any of the following measures. See Fig. 14.16 (e).
- Provide a depressed cistern having its bed below the level of the bed level of the river.
- Toe of the spillway and bed of cistern are joined by slopping glacis. See Fig. 14.17 (a).
- Providing a cistern like (i) but instead of joining toe and bed of cistern by sloping glacis, baffle walls are provided in the cistern. See Fig. 14.17 (b).
- Baffles and low weir may be provided. See Fig. 14.17 (c).
- Upturned or Ski-jump bucket is formed in the spillway structure at toe. See Fig. 14.17 (d).

**Case IV.**

- T.W.C. lies above for small discharges and below for large discharges.
- In this case, jump depth d2 is smaller than D for small discharges and larger for large discharges.
- Thus jump will remain submerged at low discharges whereas at high discharges tail water depth will be insufficient.
- In this case, a slopping apron partly below and partly above the bed level of river is constructed.
- The horizontal length of the apron is sufficiently provided.
- If need be, end sill is also provided. In this case jump will be formed at higher up
- point on the sloping apron for small discharges.
- At higher discharges the jump will be carried further on D/S side. See Figs 14.16 (c) and 14.18.

**Case V. **

- T.W.C. lies below for small discharges and above for large discharges.
- This case is just the reverse of case IV. Protective measure is also the same as in case IV.
- The formation of jump will also be reverse in order i.e. at high up points for high discharges and at lower points for low discharges.