Question

"Water is flowing through a horizontal pipe in stream line flow at the narrowest part of the pipe?"

• A. Velocity is maximum and pressure is minimum.
• B. Pressure is maximum and velocity is minimum.
• C. Both pressure and velocity are minimum.
• D. Both pressure and velocity are maximum.

Hint:

In streamline flow, as velocity increases, pressure decreases due to Bernoulli's principle.

Answer 1

The Correct Option is A

Step 1: Application of Bernoulli's principle.
Bernoulli's principle states that for an incompressible fluid in streamline flow, the total mechanical energy (pressure energy, kinetic energy, and potential energy) remains constant. Mathematically: \[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}, \] where \( P \) is pressure, \( \rho \) is fluid density, \( v \) is velocity, and \( h \) is height. Step 2: At the narrowest part of the pipe.
In a horizontal pipe: \[ P + \frac{1}{2} \rho v^2 = \text{constant}. \] At the narrowest part of the pipe, velocity (\( v \)) is maximum due to the conservation of mass (\( A_1v_1 = A_2v_2 \)). As velocity increases, pressure decreases to maintain the constant total energy. \[ \therefore \text{At the narrowest part of the pipe, velocity is maximum and pressure is minimum.} \]