In steady, incompressible flow, which equation relates pressure, velocity, and elevation head along a streamline?

In steady, incompressible flow, which equation relates pressure, velocity, and elevation head along a streamline?

• A. Bernoulli Equation
• B. Continuity Equation
• C. Fourier's Law
• D. Navier-Stokes Equation

Answer: (A)

In steady, incompressible flow where viscous losses are negligible, the energy per unit weight is conserved along a streamline. This leads to the Bernoulli relation, which ties together pressure, velocity, and elevation: p/ρg + v^2/(2g) + z = constant along a streamline (equivalently, p + ½ ρ v^2 + ρ g z = constant). This describes how increasing velocity is often accompanied by a drop in pressure, with the elevation term accounting for height in the energy balance. This is the best fit because it directly links the three quantities in question. The continuity equation concerns mass conservation and does not relate pressure to velocity and height. Fourier's law is about heat conduction. The Navier–Stokes equations describe momentum balance and include viscosity; Bernoulli is the simplified form that specifically connects pressure, velocity, and elevation under the stated assumptions.

In steady, incompressible flow where viscous losses are negligible, the energy per unit weight is conserved along a streamline. This leads to the Bernoulli relation, which ties together pressure, velocity, and elevation: p/ρg + v^2/(2g) + z = constant along a streamline (equivalently, p + ½ ρ v^2 + ρ g z = constant). This describes how increasing velocity is often accompanied by a drop in pressure, with the elevation term accounting for height in the energy balance.

This is the best fit because it directly links the three quantities in question. The continuity equation concerns mass conservation and does not relate pressure to velocity and height. Fourier's law is about heat conduction. The Navier–Stokes equations describe momentum balance and include viscosity; Bernoulli is the simplified form that specifically connects pressure, velocity, and elevation under the stated assumptions.