A deflector shown in Fig. 2.25 moves to the right at 3 m/s while the nozzle remains stationary. Determine the force components needed to move the deflector. The jet velocity is 8 m/s. The nozzle area is 2 cm x 40 cm.

Question

A deflector shown in Fig. 2.25 moves to the right at [latex]3 {m}/{s}[/latex] while the nozzle remains stationary. Determine the force components needed to move the deflector. The jet velocity is [latex]8 {m}/{s}[/latex]. The nozzle area is [latex]2 cm imes 40 cm[/latex].

Accepted Answer

Inlet triangle of velocity is a straight line as shown in Fig. 2.25(a).
The outlet triangle of velocity is shown in Fig. 2.25(b).

Bernoullis equation can be used to show that the velocity of the sheet [latex]V_{r1} = V_{r2} = 5 {m}/{s}[/latex] as observed from the deilector.

Mass flow rate is calculated on velocity [latex]V_{r1} = 5 {m}/{s}[/latex]

[latex]\dot{m} = ho AV_{r1} = 1000 imes 0.02 imes 0.4 imes 5 = 40 {kg}/{s}[/latex]

Force in the x-direction

[latex]F_{y} = Mass flow rate imes change of velocity[/latex]

[latex]F_{x} =\dot{m}\left[\left(V_{r1x} - V_{r2x} ight) ight][/latex]

[latex] = \dot{m}\left[\left(V_{r1x} - V_{r2}\cos 30^{\circ} ight) ight][/latex]

[latex]F_{x} = 40\left[5 - 5 imes 0.866 ight]=26.8 N[/latex]

[latex]F_{y} = \left[\left(V_{r1y} - V_{r2y} ight) ight] as V_{r1y} = 0[/latex]

[latex]F_{y}= - \dot{m} V_{r2y} = - \dot{m} V_{r2y} \sin 30 = - 40 imes 5 imes 0.5[/latex]

[latex] = 100 N[/latex]

Question 2.14: A deflector shown in Fig. 2.25 moves to the right at 3 m/s w...

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