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Problem 4.209 - Problem 4.209[Difficulty 3 zmax CV(b V2...

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Problem 4.209 [Difficulty: 3] z x d V 2 c e CV ( a ) CV ( b ) z max Given: Data on fire boat hose system Find: Volume flow rate of nozzle; Maximum water height; Force on boat Solution: Basic equation: First Law of Thermodynamics for a CV Assumptions: 1) Neglect losses 2) No work 3) Neglect KE at 1 4) Uniform properties at exit 5) Incompressible 6) p atm at 1 and 2 Hence for CV (a) W s V 2 2 2 g z 2 + m exit = m exit ρ V 2 A 2 = where m exit is mass flow rate (Note: Software cannot render a dot!) Hence, for V 2 (to get the flow rate) we need to solve 1 2 V 2 2 g z 2 + ρ V 2 A 2 W s = which is a cubic for V 2 ! To solve this we could ignore the gravity term, solve for velocity, and then check that the gravity term is in fact minor. Alternatively we could manually iterate, or use a calculator or Excel, to solve. The answer is V 2 114 ft s = Hence the flow rate is
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