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Question
The pressure of water inside a closed pipe is 3 × 105 N/m2. This pressure reduces to 2 × 105 N/m2 on opening the valve of the pipe. Calculate the speed of water flowing through the pipe. [Density of water = 1000 kg/m3].
Solution
Given:
p1 = 3 × 105 Pa,
v1 = 0,
p2 = 2 × 105 Pa,
ρ = 103 kg/m3
To find:
The speed of water flowing through the pipe
Solution:
Bernoulli's equation states
`"p"_1 + 1/2 rho"v"_1^2 = "p"_2 + 1/2rho"v"_2^2`
`therefore "v"_2^2 = (2 ("p"_1 - "p"_2))/rho` ....[∵ v1 = 0]
`therefore "v"_2= sqrt((2 ("p"_1 - "p"_2))/rho)`
`= sqrt((2(3 - 2) xx 10^5)/10^3)`
`= sqrt(200)`
`= 10sqrt2`
= 14.14m/s
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