Question

According to Bernoulli's theorem, for an ideal fluid the sum of pressure energy, kinetic energy and potential energy is:

• A. Variable along a streamline
• B. Zero everywhere
• C. Constant along a streamline
• D. Maximum at the inlet

Hint:

Logic Tip: Bernoulli's principle is just the "Conservation of Energy" dressed up for fluids. Since energy is conserved, the total amount of it cannot vary, become zero, or be maximum anywhere; it must remain absolutely constant along the flow path.

Answer 1

The Correct Option is C

Concept:
Bernoulli's theorem is a direct application of the principle of conservation of energy to fluid flow. It states that energy in a steady, ideal fluid flow cannot be created or destroyed, only converted from one form to another.

Step 1:
A flowing fluid possesses three primary forms of mechanical energy per unit weight (or volume): 1. Pressure energy 2. Kinetic energy (due to velocity) 3. Potential energy (due to elevation)

Step 2:
For an incompressible, non-viscous (ideal) fluid in steady flow, the equation is written as: $$ \frac{P}{\rho g} + \frac{v^2}{2g} + z = \text{Constant} $$

Step 3:
Because no energy is lost to friction (ideal fluid) and no energy is added, the total mechanical energy must remain identical at any two points along the same path of flow. Therefore, the sum is constant along a streamline.