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Question

A rotameter with a heavy float of density ρf is used for mesuring gas flow is calibrated with a gas of density (ρ) 1.5kg/m3. If it measures the flow rate of a different gas having density of 2 kg/m3 and indicates a flow rate of 10 m3/min. The actual flow rate is ________ m3/min. (Assume ρf>>ρ)

A
10 m3/min
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B
20 m3/min
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C
5 m3/min
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D
11.5 m3/min
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Solution

The correct option is D 11.5 m3/min
Equation for volume flow rate of rotameter is,

Q=Cd(AtAf)1(AtAf)2/A2t2gVf(ρfρ)ρ.Af

As Cd,At,Af,Vf are constant.

ρf>>ρ

ρfρρf

So, Q=ρfρ

Q1Q2=ρ2ρ1 [ρf=constant]

So,

Q1=Q2ρ2ρ1=1021.5=11.5 m3/min

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