Sphw5 - HOMEWORK SET 5 6.57 A small stream with 20oC water runs out over a cliff creating a 100 m tall waterfall Estimate the downstream

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HOMEWORK SET 5 6.57 A small stream with 20 o C water runs out over a cliff creating a 100 m tall waterfall. Estimate the downstream temperature when you neglect the horizontal flow velocities upstream and downstream from the waterfall. How fast was the water dropping just before it splashed into the pool at the bottom of the waterfall? Solution: CV. Waterfall, steady state. Assume no Q . nor W . Energy Eq.6.13: h + 1 2 V 2 + gZ = const. State 1: At the top zero velocity Z 1 = 100 m State 2: At the bottom just before impact, Z 2 = 0 State 3: At the bottom after impact in the pool. h 1 + 0 + gZ 1 = h 2 + 1 2 V 2 2 + 0 = h 3 + 0 + 0 Properties: h 1 h 2 same T, P => 1 2 V 2 2 = gZ 1 V 2 = 2gZ 1 = 2 × 9.806 × 100 = 44.3 m/s Energy equation from state 1 to state 3 h 3 = h 1 + gZ 1 use Δ h = C p Δ T with value from Table A.4 (liquid water) T 3 = T 1 + gZ 1 / C p = 20 + 9.806 × 100 /4180 = 20.23 ° C 6.63 A steam turbine receives steam from two boilers. One flow is 5 kg/s at 3 MPa, 700 ° C and the other flow is 15 kg/s at 800 kPa, 500 ° C. The exit state is 10 kPa, with a quality of 96%. Find the total power out of the adiabatic turbine. Solution: C.V. whole turbine steady, 2 inlets, 1 exit, no heat transfer Q . = 0 Continuity Eq.6.9: m . 1 + m . 2 = m . 3 = 5 + 15 = 20 kg/s Energy Eq.6.10: m . 1 h 1 + m . 2 h 2 = m . 3 h 3 + W . T
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Table B.1.3: h 1 = 3911.7 kJ/kg, h 2 = 3480.6 kJ/kg Table B.1.2: h 3 = 191.8 + 0.96 × 2392.8 = 2488.9 kJ/kg W T 1 2 3 W . T = 5 × 3911.7 + 15 × 3480.6 – 20 × 2488.9 = 21 990 kW = 22 MW 6.72 An automotive radiator has glycerine at 95 o C enter and return at 55 o C as shown in Fig. P6.72. Air flows in at 20
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This homework help was uploaded on 04/10/2008 for the course ME 235 taught by Professor Borgnakke during the Spring '07 term at University of Michigan.

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Sphw5 - HOMEWORK SET 5 6.57 A small stream with 20oC water runs out over a cliff creating a 100 m tall waterfall Estimate the downstream

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