Question

water flows in a horizontal constant-area pipe; the pipe diameter is 75 mm and the average flow speed is 5 m/s. At the pipe inlet, the gage pressure is 275 kpa, and the outlet is at atmoshperic pressure. determine the head loss in the pipe

Answer 1

Head loss = 28.03 m

Step-by-step explanation:

According to Bernoulli's theorem for fluids we have

`(P)/(\gamma _(w))+(V^(2))/(2g)+z=Constant`

Applying this between the 2 given points we have

`(P_(1))/(\gamma _(w))+(V_(1)^(2))/(2g)+z_(1)=(P_(2))/(\gamma _(w))+(V_(2)^(2))/(2g)+z_(2)+h_(l)`

Here
`h_(l)` is the head loss that occurs

`\therefore h_(l)=(P_(1))/(\gamma _(w))+(V_(1)^(2))/(2g)+z_(1)-(P_(2))/(\gamma _(w))-(V_(2)^(2))/(2g)-z_(2)`

Since the pipe is horizantal we have
`z_(1)-z_(2)=0`

Applying contunity equation between the 2 sections we get

`A_(1)V_(1)=A_(2)V_(2)\\\\\therefore V_(1)=V_(2)(\because A_(1)=A_(2))`

Since the cross sectional area of the both the sections is same thus the speed

is also same

Using this information in the above equation of head loss we obtain

`h_(l)=(1)/(\gamma _(w))(P_(1)-P_(2))`

Applying values we get

`h_(l)=(1)/(9810)* (275* 10^(3))m\\\\\therefore h_(l)=28.03m`