Question

The reading of the pressure meter attached with a closed pipe is 5 × 10⁵ Nm⁻². On opening the valve of the pipe, the reading of the pressure meter is 4.5 × 10⁵ Nm⁻². Calculate the speed of the water flowing in the pipe.

Answer 1

Initial pressure P₂ = 5 × 10⁵ Nm⁻²

Final pressure P₁ = 4.5 × 10⁵ Nm⁻²

Initial velocity V₁ = 0

Final velocity v₂ = v₂

Density of water ρ = 10³ kg/m³

Using Bernoulli’s theorem, we can write,

`"P"_2 + 1/2ρ"v"_2^2 = "P"_1 + 1/2ρ"v"_1^2`

`5 xx 10^5 + 1/2 xx 10^3 xx "v"_2^2 = 4.5 xx 10^5 + 1/2 xx 10^3 xx "v"_1^2`

`5 xx 10^5 - 4.5 xx 10^5 = 1/2 xx 10^3 xx "v"_2^2`

`0.5 xx 10^5 = 1/2 xx 10^3 xx "v"_2^2`

`5 xx 10^4 = (10^3"v"_2^2)/2`

`10^3"v"_2^2 = 10 xx 10^4 = 10^5`

`"v"_2^2 = 10^5/10^3 = 10^2`

∴ v₂ = `sqrt10^2` = 10 ms⁻¹

Speed of water = 10 ms⁻¹