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Unformatted text preview: Working with the HEM 1 1. (Solved on the board) Compute the pressure gradient for a saturated 1 kg s 1 steamwater flow at 7 MPa and a quality of 0.1 in a smooth 2.5 cm diameter pipe using the homogeneous equilibrium model. f TP is to be taken as f lo Assume the flow direction is upward, there is no change in quality with axial distance, and ignore the effects of gas compressibility. Well need to know viscosities and densities for both phases to complete this problem. These can be obtained from steam tables: f = 740 kg m 3 (1) v = 36 . 5 kg m 3 (2) f = 9 . 55 10 5 Pa s (3) v = 1 . 90 10 5 Pa s (4) The flow area is also required: A = D 2 4 (5) A = (0 . 025 m ) 2 4 = 0 . 0004909 m 2 (6) As are the mass flux of the mixture, G m , and the mixture density, m : G m = m A (7) G m = 1 kg s 1 . 0004909 m 2 = 2037 kg m 2 s 1 (8) m = 1 x v + 1 x f (9) m = 1 . 1 36 . 5 + 1 . 1 740 = 252 . 8 kg m 3 (10) In 1178, the second term in the numerator contains dx/dz ; it is zero since there is no phase change. The denominator becomes 1 when compressibility is ignored. The tube is round; the hydraulic diameter is simply the diameter, D . Upflow implies that cos ( ) is 1. The pressure drop relation then simplifies to: dp dz HEM = f TP D G 2 m 2 m + m g (11) We start by computing Re lo , the Reynolds number for singlephase liquid at the same mass flux in the same tube: Re lo = GD l (12) Re lo = 2037 . 025 9 . 55 10 5 = 5 10 5 (13) Working with the HEM 2 This Reynolds number is wellsuited to use of the McAdams correlation: f lo = 0 . 184 Re . 2 lo (14) f lo = 0 . 184 5 10 5 . 2 = 0 . 0132 (15) This is then substituted into Equation 11 along with the other known values: dp dz HEM = . 0132 . 025 2037 2 2 252 . 8 + 252 . 8 9 . 81 (16) dp dz HEM = dp dz HEM,fric dp dz HEM,grav (17) dp dz HEM = 4333 Pa m 1 + 2480 Pa m 1 (18) dp dz HEM = 6813 Pa m 1 (19) 2. Use Equation 1179b to compute the friction factor, employing each of the three estimates for TP (Equations 1180a through 1180c), and then use this to com pute the pressure gradient. How important is the selection of the friction factorpute the pressure gradient....
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 Fall '11
 Schubring

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