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Question

Water flows through a horizontal lobe as shown in figure , If the difference of heights of water column in the vertical lobes is 2cm and the areas of cross-section at A and B are 4cm2 and 2cm2 respectively. Find the rate of flow of water across any section.
220722_e5a3fc9adc0b4d8eb398dbf315345e21.png

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Solution

12ρv2B12ρv2A=ρg(hAhB)
or v2Bv2A=2g(hAhB)
=2×10×0.02
or v2Bv2A=0.4 m2/s2 (i)
vAAA=vBAB
or 4vA=4vB
vB=2vA
Solving Eqs. (i) and (ii), we get
vA=0.363 m/s
Volume flow rate=vAAA
=(0.365)(4×104)
=1.46×104 m3/s
=146 cm3/s

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