Assuming uniform pipe diameters, what will be the pressure drop due to kinetic energy for an incompressible fluid?

Assuming uniform pipe diameters, what will be the pressure drop due to kinetic energy for an incompressible fluid?

• A. Non-zero depending on velocity
• B. Depends on density
• C. Zero
• D. Cannot be determined

Answer: (C)

The key idea is energy balance for fluid flow. In a steady, incompressible flow through a pipe with constant diameter, the flow speed is the same at every cross-section. The kinetic-energy term in Bernoulli’s equation is ρv^2/2. Since velocity doesn’t change, this kinetic-energy contribution doesn’t change either, so there’s no pressure change tied to kinetic energy between sections. Any pressure drop comes from frictional losses along the pipe, not from a change in kinetic energy. If the diameter varied or the flow accelerated, the velocity would change and the kinetic-energy term could contribute to a pressure change; then you could see a nonzero kinetic-energy–related pressure change.

The key idea is energy balance for fluid flow. In a steady, incompressible flow through a pipe with constant diameter, the flow speed is the same at every cross-section. The kinetic-energy term in Bernoulli’s equation is ρv^2/2. Since velocity doesn’t change, this kinetic-energy contribution doesn’t change either, so there’s no pressure change tied to kinetic energy between sections. Any pressure drop comes from frictional losses along the pipe, not from a change in kinetic energy. If the diameter varied or the flow accelerated, the velocity would change and the kinetic-energy term could contribute to a pressure change; then you could see a nonzero kinetic-energy–related pressure change.