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Question

Water flows in a horizontal tube as shown in figure. The pressure of water changes by 600 N/m2 between x and y where the areas of cross - section are 3 cm2 and 1.5cm2 respectively. Find the rate of flow of water through the tube.
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A
189cm3/s
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B
159cm3/s
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C
189cm2/s
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D
159cm2/s
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Solution

The correct option is A 189cm3/s
Let the velocity at x = vx and that at y = vy.
By the equation of continuity, vyvx=3cm21.5cm2=2
By Bernoulli's equation,
Px+12pv2x=Py+12pv2y
or,PxOy=12p(2vy)212pv2y=32pv2y
or, 600Nm2=32(1000kgm3)v2x
or, vx=0.4m2/s2=0.63m/s
The rate of flow =(3cm2)(0.63m/s)=189cm3/s.

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