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Question

Kerosene oil is flowing through a pipe having constant cross section area with diameter 2.5 cm, at a rate of 10 litre/sec. The height of bottom and top end is 2 m and 8 m respectively from the datum line. Find the pressure at the lower end, if the pressure at the other end is 25×104 N/m2. (Density of kerosene =850 kg/m3)


A
2.51×104 N/m2
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B
1.51×105 N/m2
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C
2×105 N/m2
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D
3.01×105 N/m2
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Solution

The correct option is D 3.01×105 N/m2
Let the velocity and pressure at the lower end are v1 and P1 respectivley.
Let the velocity and pressure at the higher level are v2 and P2 respectively.
Given, flow of oil Q=10 litre/sec or 10×103 m3/sec
Using continuity equation,
A1v1=A1v2
but A1=A2 (uniform cross-section of tube)
v1=v2
According to the Bernoulli's theorem,
P1+12ρv21+ρgh1=P2+12ρv22+ρgh2
P1P2=12ρ(v22v21)+ρg(h2h1)
[v1=v2]
P1P2=ρg(h2h1)
P125×104=850×10×(82)
P1=301000 N/m2
P1=3.01×105 N/m2

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