Question : The reading of pressure meter attached with a closed pipe is 3.5×105 N/m2. On opening the valve of the pipe, the reading of the pressure meter is reduced to 3.0×105 N/m2. Calculate the speed of the water flowing in the pipe.
Doubt by Ananya
Solution :
P1 = 3.5×105 N/m2
P2 = 3.0×105 N/m2
V1 = 0m/s
V2 = ?
h1=h2=h
Using Bernoulli's Theorem
P1+½ρV12+ρgh1 = P2+½ρV22+ρgh2
P1+½ρ(0)2+ρgh = P2+½ρV22+ρgh
P1 = P2+½ρV22
P1-P2 = ½ρV22
2(P1-P2)/ρ = V22
P1 = P2+½ρV22
P1-P2 = ½ρV22
2(P1-P2)/ρ = V22
2(3.5×105-3.0×105)/1000 = V22
2(0.5×105)/1000 = V22
[∵ Density (ρ) of Water is 1000 kg/m³]
100 = V22
V2 = √(100)
V2 = 10 m/s
100 = V22
V2 = √(100)
V2 = 10 m/s
Hence, the speed of water flowing in the pipe is 10 m/s.