A pipe bend tapers from a diameter of dl of 500 mm at inlet to a diameter of
d2 of 250 mm at outlet and turns the flow through an angle B of 45° as
shown in Figure 1. Measurements of pressure at inlet and outlet show that
the pressure P1 at inlet is 40 kPa and the pressure P2 at outlet is 23 kPa. If the
pipe is conveying oil which has a density 850 kg/m3, calculate the
magnitude and direction of the resultant force on the bend when the oil is
flowing at the rate of 0.45 m3
/s. The bend is in a horizontal plane.