ENGG116

School of Engineering

Q2 A piping flow system is shown in Figure Q2. The fluid has density p. The pipe is circular

in cross section and the flow is steady, frictionless, incompressible and one-dimensional.

Fluid flows into the pipe at location 1 where diameter is d, and subsequently through an

expansion section at location 2 where diameter increases to D, exits the pipe at location

3 where the diameter reduces back to d. The location 2 is at elevation of H above location

1 and 3.

(a) Use the continuity equation to express the velocity at location 1 (V₁) in terms of d,

and velocity and diameter at location 2 (V₂ and D);

[4/15 marks]

(b) Use Bernoulli's equation to provide an expression for the pressure at location 2

(p2) in terms of the pressure at location 1 (p₁), V₁, d, D, A g (gravitational

acceleration) and the elevation differences between the two pipes (H);

[7/15 marks]

(c) If D = 2d and V2 = (1/7.5)gH, determine p₁ in terms of pz;

D

Figure Q2.

[4/15 marks]

H