Question

According to the Bernoulli's Theorem the sum of pressure head, velocity head, and potential head is _____________

• A. Zero
• B. Constant
• C. One
• D. Indeterminate

Hint:

To remember Bernoulli's terms:
- Pressure Head = \(\frac{p}{\rho g}\)
- Kinetic/Velocity Head = \(\frac{v^2}{2g}\)
- Potential/Datum Head = \(z\)
The sum is always constant for ideal, frictionless, steady, and incompressible fluid flows.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Bernoulli's Theorem is a fundamental principle in fluid mechanics derived from the law of conservation of energy.
It applies to an ideal fluid, which is defined as incompressible, non-viscous (frictionless), and flowing under steady, irrotational conditions along a streamline.
Key Formula or Approach:
The total energy per unit weight of a flowing fluid at any point is the sum of its pressure energy, kinetic energy, and potential energy.
Mathematically, this total energy head can be expressed as:
\[ \frac{p}{\rho g} + \frac{v^2}{2g} + z = \text{Constant} \] Where:
- \(\frac{p}{\rho g}\) is the Pressure Head (energy per unit weight due to static pressure)
- \(\frac{v^2}{2g}\) is the Velocity Head (kinetic energy per unit weight)
- \(z\) is the Potential Head or Datum Head (potential energy per unit weight due to elevation)

Step 2: Detailed Explanation:
According to Bernoulli's equation, as a fluid flows along a streamline, these three forms of energy can be continuously interconverted.
For instance, if the fluid's velocity increases (causing an increase in the velocity head), there must be a corresponding decrease in its pressure or potential head to maintain the total energy equilibrium.
This ensures that the algebraic sum of the three heads remains completely constant at every point along the flow path.
This principle is widely used to analyze flow in pipes, open channels, and in measuring devices such as Venturimeters and Pitot tubes.

Step 3: Final Answer:
According to Bernoulli's Theorem, the sum of pressure head, velocity head, and potential head is constant.