Question

The figure shows a pipe with cross-section area 10 \( cm^2 \). Water flows from one end with velocity 20 cm/s. The other end of the pipe is closed and consists of 10 holes each of area 30 \( mm^2 \). Find the velocity of water coming out from each hole: 

• A. 66 cm/s
• B. 0.66 cm/s
• C. 6.6 cm/s
• D. 66 mm/s

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem is based on the Principle of Continuity for incompressible fluids, which states that the volume flow rate (discharge) entering a system must equal the volume flow rate exiting the system.

Step 2: Key Formula or Approach:
Equation of Continuity: \[ A_1 v_1 = A_2 v_2 \] In this case, the exit area \( A_2 \) is the sum of the areas of all 10 holes.

Step 3: Detailed Explanation:
Inlet area, \( A_1 = 10 \, cm^2 \). Inlet velocity, \( v_1 = 20 \, cm/s \). Total outlet area, \( A_{total} = 10 \times 30 \, mm^2 \). Convert \( mm^2 \) to \( cm^2 \): \( 30 \, mm^2 = 0.3 \, cm^2 \). \( A_{total} = 10 \times 0.3 = 3 \, cm^2 \). Apply continuity: \[ A_1 v_1 = A_{total} v_{exit} \] \[ 10 \times 20 = 3 \times v_{exit} \] \[ 200 = 3 \times v_{exit} \] \[ v_{exit} = \frac{200}{3} \approx 66.67 \, cm/s \]

Step 4: Final Answer:
The velocity of water coming out from each hole is approximately 66 cm/s.