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. ​

Respuesta :

Answer:

-4.5 m/s

Explanation:

Assuming steady and incompressible flow and uniform properties at each section

[tex]V_1A_1+V_2A_2+A_3V_3+Q_4=0[/tex]

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

[tex]-V_1A_1+V_2A_2+A_3V_3+Q_4=0[/tex]

Making  the subject of the formula then

[tex]V_2=\frac {V_1A_1-A_3V_3-Q_4}{A_2}[/tex]

Substituting the given values then

[tex]V_2=\frac {(5\times 0.2)-(12\times 0.15)-0.1}{0.2}=-4.5 m/s\\V_2=-4.5m/s[/tex]