The pump head equation accounts for differential pressure head, velocity head, elevation head, and head losses; which equation is this?

The pump head equation accounts for differential pressure head, velocity head, elevation head, and head losses; which equation is this?

• A. Bernoulli Equation
• B. Darcy-Weisbach Equation
• C. Navier-Stokes Equations
• D. Fourier's Law

Answer: (A)

The fundamental idea is energy conservation for fluid flow along a streamline. In this form, the flow carries different forms of energy per unit weight: differential pressure energy (p/ρg), velocity energy (v^2/2g), and elevation energy (z). When fluid moves through a pipe, some energy is lost due to friction and other irreversibilities, represented by head losses. If a pump adds energy to the flow, that added energy is the pump head. Putting all of this together leads to the energy balance that describes how the total head changes from one point to another, plus the pump contribution and minus the losses. That balance is Bernoulli’s equation written in head form, extended to include head losses and pump work. It captures how the sum of pressure head, velocity head, and elevation head in the inlet plus the pump head equals the sum of those heads in the outlet plus the head losses. The other equations serve different purposes: the Darcy-Weisbach equation relates frictional pressure drop to pipe geometry and flow but doesn’t explicitly encompass all forms of energy head and pump work; the Navier-Stokes equations are the general momentum equations for viscous flow and aren’t a simple energy balance; Fourier’s law describes heat conduction.

The fundamental idea is energy conservation for fluid flow along a streamline. In this form, the flow carries different forms of energy per unit weight: differential pressure energy (p/ρg), velocity energy (v^2/2g), and elevation energy (z). When fluid moves through a pipe, some energy is lost due to friction and other irreversibilities, represented by head losses. If a pump adds energy to the flow, that added energy is the pump head. Putting all of this together leads to the energy balance that describes how the total head changes from one point to another, plus the pump contribution and minus the losses.

That balance is Bernoulli’s equation written in head form, extended to include head losses and pump work. It captures how the sum of pressure head, velocity head, and elevation head in the inlet plus the pump head equals the sum of those heads in the outlet plus the head losses.

The other equations serve different purposes: the Darcy-Weisbach equation relates frictional pressure drop to pipe geometry and flow but doesn’t explicitly encompass all forms of energy head and pump work; the Navier-Stokes equations are the general momentum equations for viscous flow and aren’t a simple energy balance; Fourier’s law describes heat conduction.