Water flows steadily from an open tank as shown in the figure below. The elevati
ID: 1423026 • Letter: W
Question
Water flows steadily from an open tank as shown in the figure below. The elevation of the water’s surface in the tank (point 1) is 15.0 m. The elevation of the exit pipe (points 2 and 3) is 4.00 m. The drain pipe narrows from a radius of 12.0 cm at point 2 to a radius of 7.25 cm at point 3. The cross sectional area of the tank is much larger than the cross sectional area of the drain pipe. (a) What is the volume flow rate in m3 /s of water draining from the tank? (0.243 m3 /s) (b) What is the pressure gage reading at point 2? (93.5 kPa)
Explanation / Answer
Water Flowing from a Tank?
Water flows steadily from an open tank
The elevation of point 1 H1 = 15.0 m,
points 2 and 3 is H2 = H3 = 4.00 m.
The cross-sectional area at point 2 A2 = 0.0480 m^2
A3 = 0.0160 m^2, where the water is discharge
The cross-sectional area of the tank is very large compared with the
cross-sectional area of the pipe.
(A) Bernoulli's equation computes discharge rate = ? m^3/s
H1 = H2 + V3^2/2g
V3 = [2g(H1 - H2)]
= [2*9.8*(10 - 2)]
= (19.6*8)
= 12.52198 m/s
Q = A3*V3
= 0.0160 * 12.52198
= 0.20 m^3/s
(B) P2 = ? Pascal
V2 = V3
H1 = H2 + P2 + V2^2/2g
P2 = H1 - H2 - V2^2/2g
= 8 - 12.52^2/2*9.8
= 0.00253 m
= 0.00253 m * (1000 kg/m^3 * 9.8 N/kg)
= 24.8 N/m^2
= 24.8 Pascals
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