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Q.

Water flows in a horizontal tube (see figure) The pressure of water change by 700  Nm−2 between A and B where the area of cross section  are  40  cm2 and  20  cm2. Respectively. Find the rate of flows of water through the tube.(density of water =1000  kgm−3)

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a

3020  cm3/s

b

2420  cm3/s

c

1810  cm3/s

d

2720  cm3/s

answer is D.

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Detailed Solution

As per Equation of Continuity, ​AAvA=ABvB​⇒40vA=20vB​⇒2vA=vBAs per Bernoulii's Principle, ​PA+12ρvA2=PB+12ρvB2 ⇒PA−PB=12ρvB2−vA2​⇒ΔP=12ρvB2−vA2   ⇒700=500vB2−vA2​⇒715=vARate of flow =  area at A x  velocity at A=40×10−4×715=27.32×10−4 m3/s= 2732  cm3/s        So the rate of flow is nearly equal to 2720 unit  .Then correct answer will be 4.
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