Problem 4.209[Difficulty: 3]zxdV2ceCV(a)CV(b)zmaxGiven:Data on fire boat hose systemFind:Volume flow rate of nozzle; Maximum water height; Force on boatSolution:Basic equation: First Law of Thermodynamics for a CVAssumptions: 1) Neglect losses 2) No work 3) Neglect KE at 1 4) Uniform properties at exit 5) Incompressible 6) patmat 1 and 2Hence for CV (a)Ws−V222g z2⋅+⎛⎜⎜⎝⎞⎠mexit⋅=mexitρV2⋅A2⋅=where mexitis mass flow rate (Note:Software cannot render a dot!)Hence, for V2(to get the flow rate) we need to solve12V22⋅g z2⋅+⎛⎜⎝⎞⎠ρ⋅V2⋅A2⋅Ws−=which is a cubic for V2!To solve this we could ignore the gravity term, solve for velocity, and then check that the gravity term is in factminor. Alternatively we could manually iterate, or use a calculator or Excel, to solve. The answer isV2114fts⋅=Hence the flow rate is
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