Question

On opposite sides of a wide vertical vessel filled with water (density \(ρ\)), two identical holes are drilled, each having cross-section area \(A\). The height difference between holes is \(x\). The resultant force of reaction of water flowing out of vessel is (\(g\) = acceleration due to gravity)

• A. \(ρAgx\)
• B. \(2ρAgx\)
• C. \(3ρAgx\)
• D. \(4ρAgx\)

Hint:

Each jet pushes the vessel back with force rho A v squared; the jets on opposite sides partly cancel.

Answer 1

The Correct Option is B

Step 1: Approach
Use momentum flow rather than pressure, and treat each jet separately.

Step 2: Each jet
Jet speed squared is $v^2=2gh$. The momentum leaving per second is $\rho Av^2=2\rho Agh$.

Step 3: Net
The jets are on opposite sides, so the vessel feels the difference: $2\rho Ag(h_2-h_1)=2\rho Agx$.

Step 4: Answer
Option (B).

Final Answer:
Each jet gives 2 rho A g h and the opposite jets subtract, so the net is 2 rho A g x, option (B). \[ \boxed{2\rho Agx} \]