CE 371 HOMEWORK 6 1 Consider the hydraulic dam shown in the

CE 371 HOMEWORK 6 1) Consider the hydraulic dam shown in the figure; releasing water at a rate of 200 m\'s into a dry river bed 50 m wide. The ground absorbs water at a rate of 0.01 m/s (velocity of the water entering the ground). Find the extent of the river that will be affected by the released water Inlet Released water n 200 mls Absorbed water Open system Water Dam Oout 50 m River bed 2) A rectangular ditch of width 10 m has a sloping bottom as shown. Water is added at the rte Q of 100 lt/s, what is dh/dt when h = 1 m? Howlong does it take for the free surface to 5 m

Solution

(a)

step 1:

Given data:

Q=200 m³/sec

b=50 m wide

V=0.01 m/sec

step 2:

according to the contunity equation,

Q=AV

200=AV

200=A(0.01)

A=20000 m²

step 3:

As it is a rectangular one,

A=LXB

20000=LX50

L=400 m

(b)

step 1:

Given data:

Q=100 lit/sec

b=10 m

slope=15 degree

step 2:

dh/dt is just the distance per unit time, in other words we can take it as velocity

just take h=1 m and proceed with the contunuity equation

100/1000=10x1xsin15xV

V=0.04 m/sec

step 3:

now we know that the velocity is distance taken per unit time, so

V=L/T

0.04=0.1/t

t=2.5 sec