Question

Head loss due to friction in a pipe carrying fluid is directly proportional to

• A. Diameter of the pipe
• B. Square of velocity of flow
• C. Density of the pipe material
• D. Area of the pipe only

Hint:

Logic Tip: The relationship is exponential, not linear. If you force water to flow twice as fast through the same pipe, the friction loss doesn't just double—it quadruples! This is why larger pipes are preferred to keep fluid velocities (and friction) manageable.

Answer 1

The Correct Option is B

Concept:
The head loss due to friction in a steady pipe flow is determined by the Darcy-Weisbach equation, which relates the energy loss to the fluid's velocity and the pipe's geometry.

Step 1: The mathematical expression for frictional head loss is the Darcy-Weisbach equation: $h_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g}$.

Step 2: In this equation, $h_f$ represents head loss, $f$ is the friction factor, $L$ is the pipe's length, $D$ is its diameter, $v$ is the flow velocity, and $g$ is the acceleration due to gravity.

Step 3: According to the numerator of the equation, the head loss ($h_f$) scales directly with the length ($L$) and the square of the flow velocity ($v^2$).

Step 4: Head loss is inversely proportional to diameter ($D$), completely unrelated to the density of the pipe's physical material, and inversely proportional to the cross-sectional area. Therefore, it is directly proportional to the square of the velocity.