Suppose the horizontal reducing bend in example 4.4.2 has an unknown bend angle (45° in ex...

Suppose the horizontal reducing bend in example 4.4.2 has an unknown bend angle (45° in example 4.4.2). What should be this bend angle so that the horizontal component force Fx is three times the vertical component force, Fy, in magnitude?

EXAMPLE 4.4.2

Water flows through a horizontal 45° reducing bend shown in Figure 4.4.3, with a 36-in diameter upstream and a 24-in diameter downstream, at the rate of 20 cfs under a pressure of 15 psi at the upstream end of the bend. Neglecting the headloss in the bend, calculate the force exerted by the water on the bend.

SOLUTION

The free-body diagram shown in Figure 4.4.3 is used. To solve this problem, equations (4.4.3) and (4.4.4) will be used:

The first objective is to determine the velocities in order to apply the energy equation to determine p2:

Next the energy equation is applied horizontally, z1 = z2 = 0 and hL = 0:

Using equation (4.4.3) yields

Using equation (4.4.4), we get

where Fy1 = 0 because there is no pressure component in the y direction at 1.

The resultant force is at an angle of θ = tan−1(4901/8517) = 30°.

Figure 4.4.3 Reducing bend for example 4.4.2.