Volume of cuboid and cylinder

Geometry Level pending

A rectangular, swimming pool of length 33m, breadth 6m, contains water to a uniform depth of 2m. The pool is emptied by means of a circular pipe of a pumpset in 10 hours. The cross-sectional radius is 10 cm. Calculate in cm/s , the speed of water flowing through the pipe?

35 cm/s 32 cm/s 30 cm/s 0.35 cm/s

Soham Pal by Soham Pal , 19, India

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1 solution

Tom Engelsman
May 16, 2021

The volumetric flow rate of the pipe computes to:

V r = 3300 c m ⋅ 600 c m ⋅ 200 c m 10 h r ⋅ 3600 s e c / h r = 11000 c m 3 / s e c \Large V_{r} = \frac{3300 cm\cdot 600 cm \cdot 200 cm }{10 hr \cdot 3600 sec/hr} = 11000 cm^{3}/sec

and the speed of the pipe's water flow computes to:

v = V r A = 11000 c m 3 / s e c π ⋅ ( 10 c m ) 2 ≈ 35 c m / s e c . \Large v = \frac{V_{r}}{A} = \frac{11000 cm^3/sec}{\pi \cdot (10 cm)^2} \approx \boxed{35 cm/sec}.

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