Question

Given below are two statements:
Statement I: Continuity equation is based on conservation of mass while Bernoulli’s equation is based on conservation of energy.
Statement II: Bernoulli’s equation is applicable to venturimeter as well as to orifice meter.
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

Remember the governing principles of fluid dynamics:
- Continuity Equation \(\rightarrow\) Conservation of Mass.
- Bernoulli's Equation \(\rightarrow\) Conservation of Energy.
- Momentum Equation \(\rightarrow\) Newton's Second Law of Motion.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Fluid dynamics relies on fundamental conservation laws.
The behavior of flowing fluids is modeled using the continuity equation (mass conservation) and Bernoulli's equation (energy conservation).
These equations are used to design and analyze flow-measuring devices.

Step 2: Detailed Explanation:
Let us evaluate both statements:
- Statement I: The continuity equation states that the mass of fluid entering a control volume must equal the mass leaving it under steady-state conditions:
\[ \rho_1 A_1 V_1 = \rho_2 A_2 V_2 \]
This is derived directly from the principle of conservation of mass.
Bernoulli's equation states that for an incompressible, inviscid fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline:
\[ P + \frac{1}{2}\rho V^2 + \rho g z = \text{constant} \]
This is a direct application of the law of conservation of energy.
Therefore, Statement I is correct.
- Statement II: Both the venturimeter and the orifice meter are differential pressure flowmeters.
They work by introducing a constriction in the flow path to increase fluid velocity, which causes a corresponding drop in static pressure.
By measuring this pressure difference, the flow rate can be determined.
The mathematical relationship used to calculate the flow rate is derived directly from Bernoulli's equation.
Therefore, Statement II is correct.
Since both statements are correct, option (A) is the correct choice.

Step 3: Final Answer:
Both Statement I and Statement II are correct.