+ -3 points My Notes Ask Your Teache Water is flowing in a pipe with a varying c

Question

+ -3 points My Notes Ask Your Teache Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.064 m2, and the magnitude of the fluid velocity is 3.50 m/s. (a) What is the fluid speed at points in the pipe where the cross section area is 0.105 m? m/s What is the fluid speed at points in the pipe where the cross section area is 0.047 m2 m/s (b) Calculate the volume of water discharged from the open end of the pipe in 1.00 hour m3 +-12 points My Notes Ask Your Teache A small circular hole 3.75 mm in diameter is cut in the side of a large water tank, 15.8 m below the water level in the tank. The top of the tank is open to the air. (a) Find the speed of efflux of the water. m/s (b) Find the volume discharged per second.

Explanation / Answer

1st Question:

Volume flow rate Q = Av = 0.064*3.5 = 0.224 m3/s

(a)

By continuity principle:

A1v1 = A2v2 = Q

=> v2(0.105) = 0.224

=> v2 = 2.13 m/s

Similarly,

v3 = 0.224/ 0.047 = 3.027 m/s

(b)

time t = 1hr = 1*60*60 s

Volume discharged = Q*t

= 0.224 *(1*60*60)

= 806.4 m3

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