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Question

Water flows through the tube shown in figure. The areas of cross section of the wide and the narrow portions of the tube are 5 cm2 and 2 cm2 respectively. The rate of flow of water through the tube is 500 cm3 s1. Find the difference of mercury levels in the U-tube.


Solution

Given Rate of flow = 500 cm3/sec

vA=(5005)=100cm/sec

VAaA=VBaB

vAvB=aBaA=25

5vA=2vB

vB=(52)vA ...(i)

12ρv2A+ρghA+pA=12ρv2B+ρghB+pB

pApB=12[p(v2Bv2A)]

h×13.6×98012×1×214(100)2

[Using (i)]

[because pApB = ?]

h=21×(100)22×13.6×980×4

= 1.969 cm 
 

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