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Question

Calculate the speed (in mm/s) of flow of glycerin at the inlet of the conical section of a pipe. If its inlet and outlet radius are 0.2 m and 0.05 m respectively. The pressure drop across its length is 10 N/m2 and density of glycerin is 1.25×103 kg/m3.

A
64.4
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B
32.6
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C
10
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D
2.6
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Solution

The correct option is B 32.6

Let speed of flow at inlet and outlet is v1 and v2. From the equation of continuity,
A1v1=A2v2
v1v2=A2A1=πr22πr21=r22r21
Inlet and outlet radius r1=0.2 m
r2=0.05 m
v1v2=(0.05)2(0.2)2=(0.25)2=0.0625
v2=16v1....(1)
Applying Bernoulli's equation,
P1+12ρv21+ρgh1=P2+12ρv22+ρgh2
v22v21=2ρ×(P1P2)
h1=h2, as tube is horizontal.
v22v21=2×101.25×103=0.016....(2)

From (1) and (2), we get
16v21v21=0.016
v21=0.01615
v1=0.0326 m/s=32.6 mm/s

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