An impoundment has a dam that has 8 mechanical gates located

An impoundment has a dam that has 8 mechanical gates located at the bottom. Each gate measures 2-feet wide by 2-feet high and their coefficient is 0.61. If the water surface elevation is 10-feet above the bottom of the dam, how long would it take to drain 25,000,000 gallons when all of the gates are fully opened?

A. 2 hrs

B. 3 hrs

C. 4 hrs

D. 5 hrs

E. 6 hrs

(What is the correct answer based on the options above?)

Solution

1 m3/s = 1000 L/s.

fluid flow rate = area of the pipe or channel×velocity of the liquid

Q = Av

Q = liquid flow rate (m3/s or L/s)

A = area of the pipe or channel (m2)

v = velocity of the liquid (m/s)

v= cv*square root of 2gh

cv= coefficient of velocity

where g=9.8 m/sec^2

so time t = av/Q= (2*2*square root of 2*9.8*10)*3600/ 25000000= 6hrs