How does fluid viscosity influence head loss in a pipe?

How does fluid viscosity influence head loss in a pipe?

• A. Higher viscosity decreases shear stresses and lowers the friction factor.
• B. Viscosity has no effect on head loss.
• C. Higher viscosity increases shear stresses, increases friction factor and head loss, reducing flow for a given pump head.
• D. Lower viscosity increases head loss.

Answer: (C)

The influential idea here is that viscosity controls how much energy is dissipated as the fluid slides along the pipe walls. In the Darcy-Weisbach form, head loss due to friction hf = f (L/D) (v^2/(2g)), the friction factor f grows with viscosity because the wall shear stress is proportional to mu times the velocity gradient at the wall. With higher mu, the same velocity profile produces greater shear at the boundary, so more energy is lost as the fluid moves along the pipe. For a given pump head, higher viscosity means more friction loss, so the system can deliver less flow. In laminar flow, the friction factor is f = 64/Re, and Re decreases as viscosity increases (for a given flow rate), which makes f larger and hf bigger. In turbulent flow, increasing viscosity lowers Re and moves the flow toward regimes with higher f for the same roughness, again increasing head loss. So increasing viscosity raises shear stresses and the friction factor, leading to greater head loss and reduced flow for a fixed pump head.

The influential idea here is that viscosity controls how much energy is dissipated as the fluid slides along the pipe walls. In the Darcy-Weisbach form, head loss due to friction hf = f (L/D) (v^2/(2g)), the friction factor f grows with viscosity because the wall shear stress is proportional to mu times the velocity gradient at the wall. With higher mu, the same velocity profile produces greater shear at the boundary, so more energy is lost as the fluid moves along the pipe.

For a given pump head, higher viscosity means more friction loss, so the system can deliver less flow. In laminar flow, the friction factor is f = 64/Re, and Re decreases as viscosity increases (for a given flow rate), which makes f larger and hf bigger. In turbulent flow, increasing viscosity lowers Re and moves the flow toward regimes with higher f for the same roughness, again increasing head loss.

So increasing viscosity raises shear stresses and the friction factor, leading to greater head loss and reduced flow for a fixed pump head.