Air ( from a 0.0508-m diameter nozzle discharge into atmosphere and becomes free

Question

Air ( from a 0.0508-m diameter nozzle discharge into atmosphere and becomes free air jet which strikes a fixed vane as shown. A total pressure tap connected to a water U-tube manometer, is located in the free air jet to measure the velocity at the nozzle exit. Ignoring friction and air weight, determine the velocity at 30? vane end and the horizontal component of the force that the air jet exerts on the vane.

What is the velocity (m/s) at 30? vane end?

What is the horizontal(x) component of the force (N) that the air jet exerts on the vane?

Explanation / Answer

from manometer

1/2 RHOa *v^2 =RHOw*g*h

1/2 *1.05*v^2 =9800*0.18 ....(RHOw*g =9800)

hence v =57.97

hence horizontal component of force is =mass flow rate *change in velocity = Q*RHOa*(V+Vcos30) ...

( +sign indicates flow is changing direction at the end)

hence horizontal component of force =3.14*(0.0508^2/4) *V*RHOa*(V+Vcos30) =13.34 N

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