Question

Water is flowing through a horizontal pipe in streamline 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, an increase in velocity corresponds to a decrease in pressure as per Bernoulli's principle. This is especially evident in areas with a smaller cross-section.

Answer 1

The Correct Option is A

Step 1: Understanding Bernoulli's principle.
Bernoulli's principle asserts that for an incompressible, non-viscous fluid in streamline flow: \[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}, \] where: \(P\): Fluid pressure, \(\rho\): Fluid density, \(v\): Fluid velocity, \(h\): Fluid height. 

Step 2: Application to a horizontal pipe. 
In a horizontal pipe (\(h\) is constant), the equation simplifies to: \[ P + \frac{1}{2} \rho v^2 = \text{constant}. \] This indicates an inverse relationship: increased fluid velocity (\(v\)) leads to decreased pressure (\(P\)), and vice versa. 

Step 3: Narrowest part of the pipe. 
At the narrowest section of the pipe: The cross-sectional area is minimal. According to the equation of continuity (\(A_1v_1 = A_2v_2\)), velocity is maximal. Consequently, by Bernoulli's principle, pressure is minimal. 

Step 4: Conclusion. 
At the pipe's narrowest point, velocity is at its maximum, and pressure is at its minimum. \[ \therefore \text{The correct answer is: (A)}. \]