Question

1. Consider the steady flow in a water pipe joint shown in the diagram. The areas are:

A1=0.2 m², A2=0.2 m², and Az=0.15 m². In addition, Fluid is lost out of a hole at
section 4, estimated at a rate of 0.1m/s. The average speed at section 1 and 3 are
Vi=5m/s and V3=12m/s, respectively. Find the velocity at section 2. ​

Answer 1

-4.5 m/s

Step-by-step explanation:

Assuming steady and incompressible flow and uniform properties at each section

`V_1A_1+V_2A_2+A_3V_3+Q_4=0`

Here V is velocity of flow and A is area, Q is flow rate out of the leak, subscript 1-4 represent different sections

At the surface, is negative hence the equation above will be

`-V_1A_1+V_2A_2+A_3V_3+Q_4=0`

Making the subject of the formula then

`V_2=\frac {V_1A_1-A_3V_3-Q_4}{A_2}`

Substituting the given values then

`V_2=\frac {(5* 0.2)-(12* 0.15)-0.1}{0.2}=-4.5 m/s\\V_2=-4.5m/s`