Question

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?

• 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 1

Answer: (A)

The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe.

Answer 2

(a): According to equation of continuity,
Av = 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.
$P+ \frac{1}{2} p v^2 = constant$
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.