Question

3. Water flows through a circular channel that has a diameter of d= 75 mm at both the inlet and outlet, as shown below. The fluid enters with uniform velocity U = 7.5 m/s. The channel makes a 90° bend that distorts the flow to produce the velocity profile at the outlet described by the function, v(r) = Vmax ( 1 -722 Assume steady, incompressible flow. Density of water is 1000 kg/m² a) Find the value of Vmax. b) Find the force that must be maintained on the elbow in the y direction in order to hold it in place. Gauge pressure at the inlet is 10 kPa, and at the outlet is 1 kPa. Neglect gravity. var)

Answer 1

Soll- All Ly vo Love VLU)= Vase City dA=21&dr lih Continuity Equation = {unda = 0 +UX 6)xt15" + Swewy- (27de) =0 USTOM ro Gran varism's umos - Sve (-3) 250 din emely ug wonglom de Nmax 220=2x7.5=15m/s)

P, =lolttokea е I P4 P2 = 102 kpa J = 7.5 m/s Momenatums Equation Eof Sv. Ceinda) along x-axis Fut PA SV. (PvdA) Font P, A = - era For 2 – P, AT PUA 2 (Pter) A = (11 kpa – 1000x75%) A 2 [11 kpa – 56.25 kPa) A From : -739.2459) + A= -12% P= 1000 kolmo A A R 2 3 Fy v bA= Sr. (evndA) along y-axis A = 2linder & Fy 2 PA+ Of van (1) (2) ar - PA+ 218 fe max) Scombrar 103X10% 4:41 -3 Pa + ax TTX1000X IS" / šed 450-24 Bant K Sa 1 2 + 2 var 40.24'* * -

450.846+ KCS-55] = 450 24 Bak - 450.84 katk SR 2 450.84 fat 1656.69 N Fy= 2107.540