Question

Consider steady flow along a streamline. If the flow satisfies the conditions necessary for the Bernoulli equation, which of the following has a constant value along the streamline?

O Static pressure
O Dynamic pressure
O Stagnation pressure
O Total pressure

Answer 1

The Bernoulli equation dictates that along a streamline in steady flow, the variable remaining constant is the total or stagnation pressure, due to the principle of conservation of energy.

Step-by-step explanation:

Considering steady flow along a streamline and the conditions necessary for the Bernoulli equation, the variable that has a constant value along the streamline is the total pressure or stagnation pressure. This follows from the principle of conservation of energy for an incompressible, frictionless fluid. The Bernoulli equation articulates that the sum of static pressure, dynamic pressure (kinetic energy per unit volume), and gravitational potential energy per unit volume remains constant along a streamline. As a fluid element moves through a streamline, increases in velocity (dynamic pressure) lead to decreases in static pressure, and vice versa, to maintain this constancy.

Out of the options given, static pressure is the quantity that has a constant value along the streamline. The static pressure represents the pressure exerted by the fluid on the walls of its container or its surroundings. It does not depend on the speed of flow or any other dynamic factors.