Question

Water flows through a 5-cm-diameter pipe at the average velocity of 1.25 m/s.

(a) In the dimensions of L/s, what is the volumetric flow rate?

(b) If the diameter of the pipe is reduced by 20% at a constriction, by what percentage does the water’s velocity change?

I need answer only in typed form. otherwise I'll downvote

Answer #1

Given

Diameter of pipe = 5cm =0.05m

Cross sectional area of pipe,

A=πd2/4

=π*(0.05*0.05)/4 =0.00196m2

Velocity of water,V=1.25m/s

a) Volumetric flow rate Q,=AV =0.00196*1.25

. =0.00245m3/s

1m3/s=10000l/s

Therefore flow rate Q= 0.00245*1000=2.45l/s

b) diameter is reduced by 20% i.e.,

d= d-20d/100 = 0.8d = 0.8*0.05 =0.04m

Area of cross section of pipe =π*0.04*0.04/4

=0.00125m2

Flow rate = 0.00245m3/s =AV

0.00245= 0.00125*V

V=0.00245/0.00125 = 1.96m/s

Therefore changed velocity= 1.96m/s

Percentage change in velocity

=(1.96-1.25)*100/1.25

=56.8%

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