The Bernoulli equation describes which quantities along a streamline?

The Bernoulli equation describes which quantities along a streamline?

• A. Pressure, temperature, and volume along a streamline
• B. Pressure, velocity, and elevation along a streamline
• C. Density, viscosity, and velocity along a streamline
• D. Pressure, density, and entropy along a streamline

Answer: (B)

Bernoulli's equation expresses conservation of mechanical energy per unit weight along a streamline for steady, incompressible, inviscid flow. The relationship P/ρ + v^2/2 + g z = constant shows that the pressure, the kinetic energy per unit mass (through velocity), and the gravitational potential energy per unit mass (through elevation z) are the quantities that trade off with each other along the path. In other words, along a streamline these three terms stay linked so that if one goes up, another must compensate to keep the sum the same. Temperature, density, viscosity, and entropy don’t appear as separate conserved terms in this simple form; they can influence whether the assumptions hold, but the basic Bernoulli relation centers on pressure, velocity, and elevation. This is why, for example, increasing velocity in a constriction must be accompanied by a drop in pressure to keep the energy balance, with elevation playing a role only if the streamline climbs or descends.

Bernoulli's equation expresses conservation of mechanical energy per unit weight along a streamline for steady, incompressible, inviscid flow. The relationship P/ρ + v^2/2 + g z = constant shows that the pressure, the kinetic energy per unit mass (through velocity), and the gravitational potential energy per unit mass (through elevation z) are the quantities that trade off with each other along the path. In other words, along a streamline these three terms stay linked so that if one goes up, another must compensate to keep the sum the same. Temperature, density, viscosity, and entropy don’t appear as separate conserved terms in this simple form; they can influence whether the assumptions hold, but the basic Bernoulli relation centers on pressure, velocity, and elevation. This is why, for example, increasing velocity in a constriction must be accompanied by a drop in pressure to keep the energy balance, with elevation playing a role only if the streamline climbs or descends.