Question

The relationship between pressure drop and velocity follows:

• A. Hooke’s law
• B. Stokes’ Law
• C. Bernoulli Law
• D. Venturi’s Law

Hint:

Bernoulli's Law explains the inverse relationship between pressure and velocity in a fluid flow. As velocity increases, pressure decreases, and this principle is essential in many fluid dynamics applications.

Answer 1

The Correct Option is C

The relationship between pressure drop and velocity is governed by Bernoulli’s Law, which is fundamental in fluid dynamics. Bernoulli's equation describes the conservation of mechanical energy in flowing fluids. It relates pressure, velocity, and elevation in a streamline flow, assuming no energy losses. Specifically, it can be written as: \[ P + \frac{1}{2} \rho v^2 + \rho gh = {constant} \] where:
- \(P\) is the pressure,
- \(\rho\) is the fluid density,
- \(v\) is the velocity,
- \(g\) is the acceleration due to gravity,
- \(h\) is the elevation.
In simpler terms, Bernoulli's principle states that as the velocity of a fluid increases, the pressure exerted by the fluid decreases, and vice versa. This relationship shows that for a given fluid, if the velocity increases in a specific region of the flow, the pressure in that region will drop. This phenomenon is important in various engineering applications, such as in aircraft wings, piping systems, and fluid transport systems. Bernoulli’s Law assumes that the flow is ideal, meaning it is incompressible and there is no energy loss due to friction.
In contrast, Hooke's law relates to elasticity, describing how materials stretch or compress under force. Stokes' law describes the motion of spherical objects through a viscous fluid, and Venturi's law deals with the flow of fluid through a constricted pipe, leading to a pressure drop and increase in velocity, but Bernoulli’s law provides a more direct and generalized explanation of the relationship between pressure and velocity.