Question

The closed-circuit wind tunnel flows air with a velocity of 200 fu's (between sections (5) and (6)] at standard condition. The picture and diagram of the wind tunnels are provided below. The flow is driven by a fan that essentially increases the static pressure by the amount Pi-P that is needed to overcome the head losses experienced by the fluid as it flows around the circuit. Determine the pressure rise ( P P ) Conditions) Assume air is incompressible (Mach number is less than 0.3); Each comer has guide vanes with a loss coefficient of K.com = 0.2; Enlarging sections from the end of the test section (6) to the beginning of the nozzle (4) as a conical diffuser with Kafle = 0.6; The loss coefficient for the conical nozzle between sections (4) and (5) and the flow straightening screens are Klozie = 0.2 and Ki.com = 4.0, respectively. Vs = 200 fts (5) (6) 71 Test section Flow straightening Screens 2013 +19) Fan Location Area (ft) Velocity (ft/s) Hint) 1. h = K. (Vº/2g) 2. When there is area change in the flow: For conical diffuser (6 to 4), the velocity in the minor loss formulation is the velocity at the inlet (section 6) For conical nozzle (4 to 5), the velocity in the formulation is the velocity at the exit (section 5)

Answer 1

Solution:

Let's first calculate all the minor losses in entire fluid flow.

1. Head loss in conical nozzle 4 to 5 = Knozzle * V² / 2g = 0.2 * 200² / 2 * 32.2 = 124.22 ft ( Hint says to take velocity at point 5 )

2. Head loss in conical diffuser 6 to 4 = Kdiffuser * V² / 2g = 0.6 * 200² / 2 * 32.2 = 372.66 ft ( Hint says to take velocity at point 6 )

3. Head loss at all the 4 corners = Kcorner * ( V2² / 2g + V3² / 2g + V7² / 2g + V8² / 2g ) = 0.2 * ( 28.6² + 22.9² + 80² + 44.4² ) / 2*32.2 = 30.167 ft

4. Head loss in flow straightening screens = Kscreen * V² / 2g = 4 * 22.9² / 2*32.2 = 32.57 ft

Assumption = Head loss in Test section 5 to 6 is negligible w.r.t. losses in other sections.

Now, Total Head loss = Summation of all the head losses = 124.22 + 372.66 + 30.167 + 32.57 = 559.617 ft

Now, p1-p9 = Density * g * total head loss = Density * 32.2 * 559.617 = density*18019.6674 ( Density of air is not given in the question, hence leaving answer in this format )