The reading of a pressure metre attached to a closed pipe is 4.5×10⁴ N m⁻². On opening the valve, water starts flowing and the reading of the pressure metre falls to 2.0×10⁴ N m⁻². The velocity of water is found to be √V m s⁻¹. The value of V is .

Question

Accepted Answer

50. Given: static reading p₁=4.5×10⁴ and flowing reading p₂=2.0×10⁴ N m⁻², water of density ρ=1000 kg m⁻³. With the valve shut the water is at rest, so the whole of the fall in the gauge reading is dynamic pressure. p₁-p₂=1/2ρ v², and p₁-p₂=2.5×10⁴ N m⁻². v²=(2(2.5×10⁴))/(1000)=50, so v=√50 m s⁻¹. Comparing with v=√V gives V=50.

The reading of a pressure metre attached to a closed pipe is 4.5×10⁴ N m⁻². On opening the valve, water starts flowing and the reading of the pressure metre falls to 2.0×10⁴ N m⁻². The velocity of water is found to be √V m s⁻¹. The value of V is ______.

Step-by-step solution