Water flows steadily from an open tank as shown in the figure. ( Figure 1 ) The

Question

Water flows steadily from an open tank as shown in the figure. (Figure 1) The elevation of point 1 is 10.0m , and the elevation of points 2 and 3 is 2.00m . The cross-sectional area at point 2 is 4.8010?2m2 ; at point 3, where the water is discharged, it is 1.6010?2m2 . The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe.

A) Assuming that Bernoulli's equation applies, compute the volume of water

?V that flows across the exit of the pipe in 1.00s . In other words, find the discharge rate ?V/?t.

Water flows steadily from an open tank as shown in the figure. (Figure 1) The elevation of point 1 is 10.0m , and the elevation of points 2 and 3 is 2.00m . The cross-sectional area at point 2 is 4.80 times 10?2m2 ; at point 3, where the water is discharged, it is 1.60 times 10?2m2 . The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe Assuming that Bernoulli's equation applies, compute the volume of water ?V that flows across the exit of the pipe in 1.00s . In other words, find the discharge rate ?V/?t.

Explanation / Answer

velocity of water through pipe

v = sqrt(2*g*h)

= sqrt(2*9.8*(10-2))

= 12.52 m/s

volume flow rate = A*v

= 1.6*10^-2*12.52

= 0.2 m^3/s


volume of the water flown in 1 s = 0.2*1 = 0.2 m^3

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