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: Bernoulli's Principle Application.
Bernoulli's principle posits that in streamline flow of an incompressible fluid, the sum of pressure energy, kinetic energy, and potential energy is constant. The mathematical representation is: \[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}, \] where \( P \) denotes pressure, \( \rho \) denotes fluid density, \( v \) denotes velocity, and \( h \) denotes height. 

Step 2: Analysis at the Narrowest Pipe Section. 
For a horizontal pipe, the equation simplifies to: \[ P + \frac{1}{2} \rho v^2 = \text{constant}. \] Due to the conservation of mass (expressed as \( A_1v_1 = A_2v_2 \)), velocity (\( v \)) reaches its peak at the pipe's narrowest section. To maintain the constant total energy, an increase in velocity results in a corresponding decrease in pressure. \[ \therefore \text{Consequently, at the narrowest section of the pipe, velocity is maximal, and pressure is minimal.} \]