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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.
Solution
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
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