Chapter 7, Problem 7.1PP

A horizontal pipe carries oil with a specific gravity of $0.83$. If two pressure gages along the pipe read $74.6$ psig and $62.2$ psig, respectively, calculate the energy loss between the two gages.

To determine

Energy loss between the two gages

Answer to Problem 7.1PP

Energy loss between the two gages is, $h_L$=34.5ft

Explanation of Solution

Given information:

S.G. of oil=0.83

Pressure at point 1, P₁= 74.6 psig

Pressure at point 1, P₂= 62.2 psig

In this problem we apply the Bernoulli's Principle or law of conservation of energy for real fluids

$\frac{P_1}{\rho g}+\frac{V_1^2}{2g}+z_1=\frac{P_2}{\rho g}+\frac{V_2^2}{2g}+z_2+h_L$

Where,

P= Pressure,

V=Velocity,

Z= Datum head,

h_L=Head loss or energy loss

Calculation:

Here we can edit the equation as per the conditions given in problem

   $\frac{P_1}{\rho g}+\frac{V_1^2}{2g}+z_1=\frac{P_2}{\rho g}+\frac{V_2^2}{2g}+z_2+h_L$

As the pipe is horizontal, so the two points in the pipe are on the same level that is, $z_1=z_2$

The cross sectional area of the pipe is uniform, so the velocity at both points is equal that is, $v_1=v_2$

After putting these values, the above equation become

   $\frac{P_1}{\rho g}=\frac{P_2}{\rho g}+h_L$

$h_L=\frac{P_1}{\rho g}-\frac{P_2}{\rho g}$= $\frac{P_1-P_2}{\rho g}$

$h_L$= $\frac{74.6-62.2}{0.03}$= 413.33in

If we want to convert inch to ft then h_Lwill be multiplied 0.083

   $h_L$=413.33inX 0.083=34.5ft

   $h_L$=34.5ft