A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?
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a
The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe.
b
Velocity and pressure both are maximum at the narrowest part of the pipe.
c
Velocity and pressure both are maximum at the widest part of the pipe.
d
The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe.
answer is A.
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Detailed Solution
According to equation of continuity, A v=constant Therefore, velocity is maximum at the narrowest part and minimum at the widest part of the pipe. According to Bernoulli's theorem for a horizontal pipe,P+12ρv2= constant Hence, when a fluid flow across a horizontal pipe of variable area of cross-section its velocity is maximum and pressure is minimum at the narrowest part and vice versa.