(a) speed of flow at point 1 m/s (b) speed of flow at point 2 m/s (c) volume flo

Question

(a) speed of flow at point 1
m/s

(b) speed of flow at point 2
m/s

(c) volume flow rate of the fluid through the pipe
m3/s

Water flows through a pipe as shown in the figure. The pressure at points 1 and 2 respectively is 1.90 x10^5 Pa and 1.15 x 10^5 Pa. The radius of the pipe at points 1 and 2 respectively is 3.20 cm and 1.30 cm. If the vertical distance between points 1 and 2 is 2.75 m, determine the following. (a) speed of flow at point 1 m/s (b) speed of flow at point 2 m/s (c) volume flow rate of the fluid through the pipe m^3/s

Explanation / Answer

COntinuity equation

A1V1=A2V2

pi*r1^2*V1=pi*r2^2*V2

V2=6.06*V1

now from bernoulli equation

P1+1/2*rho*V1^2=P2+1/2*rho*V2^2+rho*g*H

P1+1/2*rho*V1^2=P2+1/2*rho*36.71V1^2+rho*g*H

1.9*10^5+1/2*1000*V1^2=1.15*10^5+1/2*1000*36.71*V1^2+1000*9.81*2.75

a.)V1=1.64 m/s

b.)V2=6.06V1

=9.94 m/s

c.)Volume flow rate =A1*V1

=pi*0.032^2*1.64

=5.27*10^-3 m^3/s ans

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