Question

In a horizontal pipe, velocity doubles. Pressure gets

• A. Unchanged
• B. Decreased
• C. Increased
• D. Doubled

Hint:

As velocity ($V$) increases, kinetic energy increases. To keep the total energy constant in a horizontal flow, the static pressure ($P$) must decrease.
This is the fundamental principle behind Venturi tubes and aerodynamic lift.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks what happens to the static pressure of a fluid flowing in a horizontal pipe when its velocity is doubled.

Step 2: Key Formula or Approach:
We use Bernoulli's equation for steady, incompressible, frictionless flow along a horizontal streamline (where elevation $z$ is constant):
\[ P_1 + \frac{1}{2}\rho V_1^2 = P_2 + \frac{1}{2}\rho V_2^2 \]

Step 3: Detailed Explanation:

• Let the initial pressure and velocity be $P_1$ and $V_1$.

• The final velocity is doubled, so $V_2 = 2V_1$.

• Substitute $V_2$ into Bernoulli's equation:
\[ P_2 = P_1 + \frac{1}{2}\rho V_1^2 - \frac{1}{2}\rho (2V_1)^2 \]
\[ P_2 = P_1 + \frac{1}{2}\rho V_1^2 - \frac{4}{2}\rho V_1^2 \]
\[ P_2 = P_1 - \frac{3}{2}\rho V_1^2 \]

• Because the term $\frac{3}{2}\rho V_1^2$ is strictly positive for any flowing fluid, the final static pressure $P_2$ must be less than the initial static pressure $P_1$.

• This demonstrates that an increase in kinetic energy (due to doubling the velocity) causes a corresponding decrease in static pressure.

Step 4: Final Answer:
The static pressure gets decreased.