Question about fluid flows!?

Question

A fluid of specific gravity 0.8 flows at a flow rate of 35kg/s in a horizontal pipe of 200mm diameter that reduces to 150mm diameter..

Calculate the average velocities with which the fluid travels in the two sections of pipe.

i. Assuming that there are no losses in the pipe, what is the difference in pressure between the two sections of the pipe ?

Can someone show me how to tackle this question please?

Answer 1

specific gravity ,SG=0.8

Mass flow rate,m(dot)=35 kg/s

Initial diameter,d1=200 mm=0.2 m

Final diameter,d2=150 mm=0.15 m

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m(dot)=rho*A1*v1

m(dot)=(1000SG)*(pi/4*d1^2)*v1

35=1000*0.8*pi/4*0.2^2*v1

v1=1.3926 m/s

Using continuity equation

A1v1=A2v2

d1^2*v1=d2^2*v2

v2=(d1^2/d2^2)*v1

    =(0.2^2/0.15^2)*1.3926

    =2.476 m/s

v2=2.476 m/s

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Use the Bernoulli's equation

(delta p/Rho)=(v1^2-v2^2)/2g

delta p=Rho*(v1^2-v2^2)/2g

            =1000*0.8*(1.3926^2-2.476^2)/(2*9.81)

           =-3352.99 Pa

            =-3.353 kPa

Flow is from 1 to 2