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

Answer:

Head loss = 28.03 m

Explanation:

According to Bernoulli's theorem for fluids  we have

$\frac{P}{\gamma _{w}}+\frac{V^{2}}{2g}+z=Constant$

Applying this between the 2 given points we have

$\frac{P_{1}}{\gamma _{w}}+\frac{V_{1}^{2}}{2g}+z_{1}=\frac{P_{2}}{\gamma _{w}}+\frac{V_{2}^{2}}{2g}+z_{2}+h_{l}$

Here $h_{l}$ is the head loss that occurs

$\therefore h_{l}=\frac{P_{1}}{\gamma _{w}}+\frac{V_{1}^{2}}{2g}+z_{1}-\frac{P_{2}}{\gamma _{w}}-\frac{V_{2}^{2}}{2g}-z_{2}$

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

$h_{l}=\frac{1}{\gamma _{w}}(P_{1}-P_{2})$

Applying values we get

$h_{l}=\frac{1}{9810}\times (275\times 10^{3})m\\\\\therefore h_{l}=28.03m$