Question

The equation which expresses the energy balance for fluid flow is -------.

• A. Continuity equation
• B. Bernoulli's equation
• C. Fourier equation
• D. Plank's equation

Hint:

Remember:
- Continuity Equation \(\rightarrow\) Conservation of Mass
- Bernoulli's Equation \(\rightarrow\) Conservation of Energy

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Fluid flow is governed by three fundamental conservation laws: conservation of mass, conservation of momentum, and conservation of energy.

Step 2: Detailed Explanation:
Let us identify the physical conservation law associated with each equation:
1. Continuity equation: Derived from the law of conservation of mass, stating that the mass entering a system must equal the mass leaving the system under steady-state conditions (\(A_1 V_1 = A_2 V_2\)).
2. Bernoulli's equation: Derived from the conservation of energy for an incompressible, inviscid, steady, and irrotational fluid flow along a streamline. It sums pressure energy, kinetic energy, and potential energy per unit volume:
\[ P + \frac{1}{2}\rho V^2 + \rho g z = \text{Constant} \]
3. Fourier equation: Governs the rate of heat conduction (energy transfer via heat).
4. Planck's equation: Quantifies the energy of electromagnetic radiation (\(E = h\nu\)).

Step 3: Final Answer:
Bernoulli's equation is the energy balance equation for fluid flow.