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CE 230-Engineering Fluid Mechanics Lecture # 22-24 MOMENTUM EQUATION Time rate of change of a system extensive property = time rate of change of that property in CV + Net outflow rate of that property across CS Momentum equation Select B=linear momentum=m V Therefore b = V d [mV ] VdV V (V . A) dt t cv cs Time rate of change of system L.M.= TROC of L.M. in C.V+Net outflow of L.M.C.S. Special case: steady flow the momentum equation is F V (V . A) cs Note that these are three equation LHS = all forces acting on fluid in c.v. Including body, surface and external forces Applications of ME to be examined Forces on nozzles Forces on bends Forces from jets Forces on sluice gates Problem 6.39 Determine the components of the force needed to hold the bend nozzle in place. V=130 ft/s Nozzle weight = 100lb Problem 6.53 What if we have double nozzle? Given V’s and sizes. Q= 0.5m3/s Va=Vb Ra=5cm Rb=6cm Forces on bends Example 6.7 z x Forces resulting from jets Determine the force created by the steam jet on the blade. What if the blade was moving along x with a velocity of 100m/s Force on a sluice gate 6.3 Jet dia and v are given so is weight of tank and water Need forces needed to hold tank V = 20m/s D=30mm