Question

Water flows steadily through a horizontal pipe from point \(1\) to point \(2\). At point \(1\), the velocity is \(2\ \text{m/s}\) and the pressure is \(300\ \text{kPa}\). At point \(2\), the velocity is \(4\ \text{m/s}\) and the height difference between the points is negligible. The density of water is \(1000\ \text{kg/m}^3\). The pressure at point \(2\) is

• A. \(304\ \text{kPa}\)
• B. \(294\ \text{kPa}\)
• C. \(296\ \text{kPa}\)
• D. \(300\ \text{kPa}\)

Hint:

For a horizontal streamline, \[ \boxed{ P+\frac12\rho V^2=\text{constant}. } \] Thus, \[ \boxed{ \text{Higher velocity} \Longrightarrow \text{Lower pressure}. } \]

Answer 1

The Correct Option is B

Step 1: Apply Bernoulli's equation. For steady incompressible flow in a horizontal pipe, \[ P_1+\frac12\rho V_1^2 = P_2+\frac12\rho V_2^2. \] Since the pipe is horizontal, \[ z_1=z_2. \]

Step 2: Substitute the given values. Given, \[ P_1=300\ \text{kPa}=300000\ \text{Pa}, \] \[ V_1=2\ \text{m/s}, \] \[ V_2=4\ \text{m/s}, \] \[ \rho=1000\ \text{kg/m}^3. \] Hence, \[ P_2 = 300000 + \frac12(1000)(2^2-4^2). \] \[ = 300000 + 500(4-16). \] \[ = 300000 -6000. \] \[ = 294000\ \text{Pa}. \] Therefore, \[ P_2 = 294\ \text{kPa}. \] Hence, \[ \boxed{294\ \text{kPa}} \] is the correct answer. Thus, \[ \boxed{(B)} \] is the correct answer.