Answer to Question #232713 in Chemical Engineering for Victor

Question

Consider the steady flow in University of Abuja water pipe joint shown in the diagram. The areas are: A1=0.3 m2, A2= 0.3 m2, and A3=0.25 m2. In addition, fluid is lost out of a hole at estimated rate of 0.2 m3/s. The average speeds at sections 1 and 3 are V1=10 m/s and V3= 24 m/s respectively. Find the velocity at section 2, assumption made should be duly stated also as an engineer in the making; interpret your final result using engineering intuition.

Answer 1

By the conservation of mass and continuity equation

Let Q₂ be in the upward direction

$Q_1+Q_2=Q_4+Q_3\\ A_1V_1+A_2V_2=A_4V_4+A_3V_3\\ 0.3*8+0.3V_2=0.1+0.2*12\\ V_2= \frac{0.1+0.2*12}{0.3}\\ V_2=0.333 m/s$

Velocity V₂ = 0.333 m/s and in the direction is upwards at 2