04waterjet

# 04waterjet - Waterjet first draft from Prof Carmichael...

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Waterjet first draft 9/23/04 from Prof. Carmichael notes. 9/17/06: modified to reflect w (V=>V A ) and separate inlet and outlet pressure loss (in addition to drag) to reflect paper V A velocity inlet w wake fraction Vs ship velocity Vj nozzle (outlet) velocity V A := V s (1 w) T = m_dot ( V J V A ) m_dot = mass_flow_rate d h Vj V A ρ g d at inlet centerline . .. p local = p atmos + at this point . .. total pressure (pitot tube) p oin = p local + 1 ⋅ρ⋅ V A 2 = p atmos + ρ⋅ g d + 1 ⋅ρ⋅ V A 2 2 2 pressure at inlet to pump . .. 1 2 total pressure (pitot tube) . .. p op = p oin ρ⋅ g (d + h) = p atmos ρ⋅ g h + 2 ⋅ρ⋅ V A pressure at pump exit. .. total p oj = p atmos + 1 2 ⋅ρ⋅ V j 2 pressure (pitot tube) . . total pressure increase across pump . .. p oj p op = p atmos + 2 1 ⋅ρ⋅ V j 2 p atmos + ρ⋅ g h 2 1 ⋅ρ⋅ V A 2 = 2 1 ⋅ρ⋅ V j 2 V A 2 + ρ⋅ g h energy rise across the pump p oj p op 1 2 2 per unit mass flow is . .. ρ = 2 V j V A + gh power absorbed by ideal pump is p oj p op 1 2 2 therefore . .. P pi = m_dot ρ = m_dot 2 V j V A + gh ideal efficiency is then . .. and quasi propulsive coefficient is . .. ) T P Ti effective_power P E RV s (1 t V s 1 t TV A 1 t P Ti 1 t η i = η D = = = = = = = ⋅η i P pi power_delivered P pi P Pi P Pi 1 w P Pi 1 w P pi 1 w V J P Ti TV A m_dot V A V J ) 2V A V J ) 2V

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04waterjet - Waterjet first draft from Prof Carmichael...

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