Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Bernoulli's theorem
Question Statement:
Which of the following physical assumptions are strictly required for the classical Bernoulli energy equation $\frac{p}{\rho g} + \frac{v^2}{2 g} + z = \text{constant}$ to hold valid along a streamline?
Options:
(A) The fluid is ideal (inviscid, having zero viscosity and zero frictional shear losses)
(B) The flow is steady, meaning local temporal velocity fluctuations $\frac{\partial v}{\partial t} = 0$
(C) The fluid is incompressible, maintaining a strictly constant fluid density $\rho$
(D) The flow must be violently turbulent to promote isotropic kinetic dissipation across streamlines
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
- Statements A, B, and C are essential classical conditions for Bernoulli's equation derived from Euler's equation along a streamline:
1. Inviscid flow (no viscous shear losses).
2. Steady flow (no partial time derivatives).
3. Incompressible flow (constant mass density $\rho$).
4. Irrotational flow allows the constant to be identical throughout the whole fluid field; otherwise, it is constant along each streamline.
- Statement D is false because turbulence introduces substantial energy dissipation, violating the inviscid conservation assumption.