Section 4: Soil and Water Conservation Engineering
Dynamics of Flow & Bernoulli Equation
Subtopic: Assumptions of Bernoulli equation
Question Statement:
Bernoulli's energy equation along a streamline $\frac{P}{\rho g} + \frac{v^2}{2g} + z = \text{constant}$ is derived under which set of fundamental assumptions?
Options:
(A) Steady, incompressible, frictionless (inviscid), and along a streamline
(B) Unsteady, compressible, irrotational, and viscous
(C) Steady, compressible, turbulent, and along a streamline
(D) Incompressible, unsteady, rotational, and boundary-layer flow
Answer Key:
A
Step-by-Step Solution & Explanation
Bernoulli's equation is derived by integrating Euler's equation of motion along a streamline under the four core assumptions:
1. Steady flow ($\partial/\partial t = 0$)
2. Incompressible fluid ($\rho = \text{constant}$)
3. Frictionless / inviscid fluid (shear stress $\tau = 0$)
4. Flow along a streamline.