Question

Find pressure difference between A and B.

• A. \(75\,MPa\)
• B. \(85\,MPa\)
• C. \(95\,MPa\)
• D. \(65\,MPa\)

Answer 1

The Correct Option is A

Concept: Using Bernoulli's theorem for fluid flow at same height: \[ P + \frac{1}{2}\rho v^2 = \text{constant} \] Also apply continuity equation: \[ A_A v_A = A_B v_B \]
Step 1:Apply continuity equation. Convert areas: \[ A_A = 10\,cm^2 = 10 \times 10^{-4} m^2 \] \[ A_B = 20\,mm^2 = 20 \times 10^{-6} m^2 \] \[ A_A v_A = A_B v_B \] \[ (10\times10^{-4})(10) = (20\times10^{-6})v_B \] \[ v_B = 500\,m/s \]
Step 2:Apply Bernoulli's equation. \[ P_A + \frac{1}{2}\rho v_A^2 = P_B + \frac{1}{2}\rho v_B^2 \]
Step 3:Find pressure difference. \[ P_A - P_B = \frac{1}{2}\rho (v_B^2 - v_A^2) \] \[ P_A - P_B = \frac{1}{2}(600)\left(500^2 - 10^2\right) \] \[ P_A - P_B = 7.497\times10^7\,Pa \] \[ P_A - P_B \approx 75\,MPa \] \[ \boxed{75\,MPa} \]