A 1-in-diameter jet of water having a velocity of 20 ft/s is deflected 90° by a curved vane, as shown in Fig. 16.3. The jet flows freely in the atmosphere in a horizontal plane. Calculate the x and y forces exerted on the water by the vane. deflection h is 7.40 in. Compute the velocity of flow

Question

A 1-in-diameter jet of water having a velocity of 20 ft/s is deflected 90° by a curved vane, as shown in Fig. 16.3. The jet flows freely in the atmosphere in a horizontal plane. Calculate the x and y forces exerted on the water by the vane. deflection h is 7.40 in. Compute the velocity of flow in the pipe and the volume flow rate in gal/min.

Accepted Answer

Using the force diagram of Fig. 16.4, we can write the force equation for the x direction as

[latex] F_x = ho Q \left(v_{2_x}-v_{1_x} ight) [/latex]

[latex] R_x = ho Q \left[0-\left(-v_1 ight) ight] = ho Q v_1[/latex]

We know that

[latex] Q = Av = \left(0.00545ft^2 ight) \left(20ft/s ight) = 0.109ft^3/s[/latex]

Then, assuming [latex] ho = 1.94 slugs/ft^3 = 1.94lb·s^2/ft^4[/latex] , we write

[latex] R_x = ho Qv_1 = \frac{1.94lb·s^2}{ft^4} imes \frac{0.109ft^3}{s} imes \frac{20ft}{s} = 4.23lb [/latex]

For the y direction, assuming [latex] v_2 = v_1[/latex], the force is

[latex] F_y = ho Q\left(v_{2_y}-v_{1_y} ight) [/latex]

[latex]R_y = ho Q\left(v_2-0 ight) = \left(1.94 ight) \left(0.109 ight) \left(20 ight) lb = 4.23lb[/latex]

Question 16.1: A 1-in-diameter jet of water having a velocity of 20 ft/s is...

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