Engineering Words Math MASS Conservation Mass m =  V Rate of mass accumulation in system + Net rate of mass flow OUT of system = 0 n V A h l b IN1 IN2 OUT1 OUT2 Q = VA Words-Math-Engineering Lets us define a discharge as Always positive IN is any opening on the system Where there is a net flow IN OUT is any opening on the system Where there is a net flow out If flow is normal to an opening of Area A --- Q = vA

Engineering Words Math Momentum Balance Force = Mass X Acceleration OR Force = Rate of Change of Momentum OR Rate of accumulation n Rate of Momentum accumulation in system + Net rate of Momentum flow OUT of system = Sum of external Forces Applied on System Momentum = mass X Velocity n V A Nozzle See ex 6.3, 194 In Out x: direction Force Balance FxFx FyFy What are the forces required to keep nozzle in place = 0 in this case (steady) Lets us define a discharge as Gauge pressure y: direction In this case Left hand side is zero Look at examples 6.5 page 198,

Example 6.9 Block Sliding at constant velocity in x-direction v b Motion induced by water jet with speed v j 1 2 Two frames of Reference A Fixed Observer sees an x-velocity v j entering cart and an x-velocity v b Leaving Net momentum out = Net x-momentum out of volume = Frictional Force Q 1 = Q 2 =(v j –v b )A j An Observer on the cart sees an x-velocity (v j – v b ) entering cart and an x-velocity 0 Leaving Net momentum out = So, although the calculation has different steps, the net momentum out is independent of the frame of reference—If frame is an inertial frame—can move BUT has NO acceleration