(a) Explanation The figure below represents the stream 1 , stream 2 , stream 3 and stream 4 . Figure-(1) Write the expression for mass balance for water vapor. m ˙ v 1 + m ˙ v 2 + m ˙ w = m ˙ v 3 m ˙ w = m ˙ v 3 − m ˙ v 1 − m ˙ v 2 (I) Here, mass flow rate of vapor of stream 1 is m ˙ v 1 , mass flow rate of vapor of stream 2 is m ˙ v 2 , mass flow rate of vapor of stream 3 is m ˙ v 3 and mass flow rate of liquid entering is m ˙ w . Write the expression for mass flow of air balance at steady state. m ˙ a 1 + m ˙ a 2 = m ˙ a 3 (II) Here, mass flow rate of air of stream 1 is m ˙ a 1 , mass flow rate of air of stream 2 is m ˙ a 2 and mass flow rate of air of stream 3 is m ˙ a 3 Write the expression for mass flow rate of vapor stream 1 m ˙ v 1 = ω 1 m ˙ a 1 (III) Here, mass flow rate of air of stream 1 is m ˙ a 1 and humidity ratio of stream 1 is ω 1 . Write the expression for mass flow rate of vapor of stream 2 m ˙ v 2 = ω 2 m ˙ a 2 (IV) Here, mass flow rate of air of stream 2 is m ˙ a 2 and humidity ratio of stream 2 is ω 2 . Write the expression for mass flow rate of vapor of stream 3 m ˙ v 3 = ω 3 m ˙ a 3 (V) Here, mass flow rate of air of stream 3 is m ˙ a 3 and humidity ratio of stream 3 is ω 3 . Write the expression for partial pressure of water vapor of stream 1 . p v 1 = ϕ 1 p g 1 (VI) Here, relative humidity of water vapor of stream 1 is ϕ 1 and saturated pressure of water vapor of stream 1 is p g 1 . Write the expression for partial pressure of water vapor of stream 2 . p v 2 = ϕ 2 p g 2 (VII) Here, relative humidity of water vapor of stream 2 is ϕ 2 and saturated pressure of water vapor of stream 2 is p g 2 . Write the expression for partial pressure of water vapor of stream 3 . p v 3 = ϕ 3 p g 3 (VIII) Here, relative humidity of water vapor of stream 3 is ϕ 3 and saturated pressure of water vapor of stream 3 is p g 3 . Write the expression for humidity ratio of stream 1 . ω 1 = 0.622 p v 1 p t − p v 1 (IX) Here, partial pressure of water vapor of stream 1 is p v 1 and total pressure is p t . Write the expression for humidity ratio of stream 2 . ω 2 = 0.622 p v 2 p t − p v 2 (X) Here, partial pressure of water vapor of stream 2 is p v 2 and total pressure is p t . Write the expression for humidity ratio of stream 3 . ω 3 = 0.622 p v 3 p t − p v 3 (XI) Here, partial pressure of water vapor of stream 3 is p v 3 and total pressure is p t . Write the expression for mass flow rate of dry air of stream 1 . m ˙ a 1 = p t − p v 1 R T 1 ( V ˙ 1 ) (XII) Here, partial pressure of water vapor of stream 1 is p v 1 and total pressure is p t , characteristic gas constant is R , volume flow rate of stream 1 is V ˙ 1 and temperature of stream 1 is T 1 . Write the expression for mass flow rate of dry air at stream 2 . m ˙ a 2 = p t − p v 2 R T 2 ( V ˙ 2 ) (XIII) Here, partial pressure of water vapor of stream 2 is p v 2 and total pressure is p t , characteristic gas constant is R , volume flow rate of stream 2 is V ˙ 2 and temperature of stream 2 is T 2 . Write the expression for mass flow rate of dry air of stream 3 . m ˙ a 3 = p t − p v 3 R T 3 ( V ˙ 3 ) (XIV) Here, partial pressure of water vapor of stream 3 is p v 3 and total pressure is p t , characteristic gas constant is R , volume flow rate of stream 1 is V ˙ 3 and temperature at stream 3 is T 3 . Write the expression for energy balance to the system for steady stream. 0 = Q ˙ C V − W C V + [ ( m ˙ a 1 h a 1 + m ˙ v 1 h v 1 ) + ( m ˙ a 2 h a 2 + m ˙ v 2 h v 2 ) + m ˙ w h 4 ] − ( m ˙ a 3 h a 3 + m ˙ v 3 h v 3 ) (XV) Here, the rate of heat transfer is Q ˙ C V , the rate of work transfer is W C V , mass flow rate of air of stream 1 is m ˙ a 1 , mass flow rate of air of stream 2 is m ˙ a 2 , mass flow rate of air of stream 3 is m ˙ a 3 , enthalpy of air of stream 2 is h a 2 , enthalpy of air of stream 3 is h a 3 , enthalpy of air of stream 1 is h a 1 , mass flow rate of vapor of stream 1 is m ˙ v 1 , mass flow rate of vapor of stream 2 is m ˙ v 2 , mass flow rate of vapor of stream 3 is m ˙ v 3 and mass flow rate of liquid entering is m ˙ w , enthalpy of vapor is of stream 1 is h v 1 , enthalpy of vapor of stream 2 is h a 2 , enthalpy of vapor is of stream 3 is h v 3 and enthalpy of liquid entering is h w . Conclusion: Refer to Table A-2E, “Properties of saturated water(liquid-vapor):temperature table”, to obtain saturated pressure of water vapor corresponding to temperature 40 °F as 0.1217 lbf / in 2 , saturated pressure of water vapor corresponding to temperature 60 °F as 0.2563 lbf / in 2 . Write the formula of interpolation method of two variables. y 2 = ( x 2 − x 1 ) ( y 3 − y 1 ) ( x 3 − x 1 ) + y 1 (XVI) Here, the variables denote by x and y are temperature and saturated pressure of water vapor. Show the temperature at 84 °F and 86 °F as in Table (1). Temperature, °F Saturated water vapour pressure, lbf / in 2 84 0.5776 85 y 2 86 0.6158 Substitute 85 °F for x 2 , 84 °F for x 1 , 86 °F for x 3 , 0.6158 lbf / in 2 for y 3 and 0.5776 lbf / in 2 for y 1 in Equation (XVI). y 2 = [ ( 85 °F − 84 °F ) ( 0.6158 lbf / in 2 − 0.5776 lbf / in 2 ) ( 86 °F − 84 °F ) + 0.5776 lbf / in 2 ] = ( 0.0382 lbf / in 2 ) 2 + 0.5776 lbf / in 2 = 0.5967 lbf / in 2 (XVII) Substitute 0.1217 lbf / in 2 for p g 1 and 0.8 for ϕ 1 in Equation (VI). p v 1 = 0.8 × 0.1217 lbf / in 2 = 0.09736 lbf / in 2 (XVIII) Substitute 0.2563 lbf / in 2 for p g 2 and 0.8 for ϕ 2 in Equation (VII). p v 2 = 0.8 × 0.2563 lbf / in 2 = 0.20504 lbf / in 2 (XIX) Substitute 0.5967 lbf / in 2 for p g 3 and 0.35 for ϕ 3 in Equation (VIII). p v 3 = 0.35 × 0.5967 lbf / in 2 = 0.208845 lbf / in 2 (XX) Substitute 14.7 lbf / in 2 for p t and 0.09736 lbf / in 2 for p v 1 in Equation (IX). ω 1 = 0.622 0.09736 lbf / in 2 14.7 lbf / in 2 − 0.09736 lbf / in 2 = 0.622 0.09736 lbf / in 2 14.60264 lbf / in 2 = 0.004147 kg of vapor / kg of air (XXI) Substitute 14.7 lbf / in 2 for p t and 0.20504 lbf / in 2 for p v 2 in Equation (X). ω 2 = 0.622 0.20504 lbf / in 2 14.7 lbf / in 2 − 0.20504 lbf / in 2 = 0.622 0.20504 lbf / in 2 14.49496 lbf / in 2 = 0.00879 kg of vapor / kg of air (XXII) Substitute 14.7 lbf / in 2 for p t and 0 (b) To determine The rate at which liquid water is injected.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 12.9, Problem 91P

(a)

To determine

The rate of heat transfer to the device.

(b)

To determine

The rate at which liquid water is injected.

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Chapter 12.9, Problem 89P

Chapter 12.9, Problem 92P

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