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A pipe is running full of water. At a point A, its diameter is 55cm, from where it tapers to 15cm diameter at B. The pressure difference between A and B is 98cm of water column. Find rate of flow of water through pipe.

A pipe is running full of water. At a point A, its diameter is 55cm, from where it tapers to 15cm diameter at B. The pressure difference between A and B is 98cm of water column. Find rate of flow of water through pipe.

Grade:11

2 Answers

Nirmal Singh.
askIITians Faculty 44 Points
7 years ago
by principle; of continuity A1*v1 = A1*v2
pi*r1^2*v1 = pi*r2^2*v2
(d1 /2)^2*v1 = (d2/2)^2*v^2
v1/v2 = d2^2 /d1^2
v1/v2 = (15/55)^2 = (0.27273)^2 =0.07438-------------------(i)
P1 -P2 = rho*g*h = 1000*9.8*98x10^-2 = 9604 N/m^2
by Bernoulli Theo rum
P1-P2 = 1/2*rho*(v2^2 - v1^2) = 9604
1/2*1000*(v2^2 - v1^2) = 9604
v2^2 - v1^2 =19.21 -----------------------(ii)
by solving (i) and (ii)
v1 = 0.32727 m/s , v2 = 4.4 m/s
Thanks & Regards,
Nirmal Singh
Askiitians Faculty
chaitnyakishore
26 Points
7 years ago
Sir I asked the rate of flow, but you gave the velocities. if v1=o.32727 m/s, v2=.4.4 m/s, d1=55cm, d2=15cm Therefore rate of flow A1v1=A2v2= p(d1)²v1/4 =(22×0.55²×0.32727)/(7×4) =0.077785066 m^3/s

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