Question

Water is flowing through a horizontal pipe of non-uniform cross-section. In the region of narrowest part inside the pipe, the water will have

• A. maximum velocity and minimum pressure.
• B. both the pressure and velocity maximum.
• C. both the pressure and velocity minimum.
• D. maximum pressure and minimum velocity.

Hint:

In fluid flow, higher speed always corresponds to lower pressure in horizontal pipes.

Answer 1

The Correct Option is A

Step 1: Continuity equation.
For incompressible fluid:
\[ A v = \text{constant} \] Thus, velocity is maximum where cross-sectional area is minimum.

Step 2: Bernoulli’s theorem.
For horizontal flow:
\[ P + \frac{1}{2}\rho v^2 = \text{constant} \]
Step 3: Pressure–velocity relation.
Increase in velocity causes decrease in pressure.

Step 4: Conclusion.
At the narrowest part of the pipe, velocity is maximum and pressure is minimum.