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Question

If it takes 5 minutes to fill a 15L bucket from a water tap of diameter 2π cm then the Reynolds number for the flow is (density of water = 103kg/m3 and visocsity of water =103Pa.s) close to.

A
11,000
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B
550
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C
1100
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D
5500
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Solution

The correct option is D 5500
The velocity can be determined from Q=Av...(i) where Q is volume flow rate, A and V are area and velocity of tube.
Given V=15L=15×103m3,A=πD24=π0.02π24=104m2
V=Qt
Q=Vt=15×10360×5=0.5×104m3/s
Using Q in equation (i)
v=QA=0.5×104104=0.5m/s
Reynolds number for flow in a tube is given as Rn=vDν where ν is kinematic viscosity of fluid.
Rn=vDμρ where μ is viscosity of fluid
Rn=0.50.02π×103103
Rn=5649 hence correct answer is option D

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