Document 5kpQnxr5kVKoq0Bn6o6nzvwN4

78 CHAPTER 4 1946 Guide Fig. 5. Comparison of Velocity Profiles for 3 Different Reynolds Numbers but for Same Average Velocity factor in turbulent flow, is open to some conjecture; artificially roughened pipes, for instance, give results at. variance with actual tests. The curves above the smooth pipe curve of Fig. 4 represent a summary of tests on rough pipe, each of them, identified by a value of e/d, with e signifying the absolute roughness in feet. Values of e/d for different pipes are given in Table 1. ' To find the friction loss for any. pipe, follow the curve with the proper value of e/d, to the pertinent value of Nrc; and from this point proceed horizontally, to left margin, to find the value of / to use in Equation 5. . Equation 5 is applicable to all liquids, and to gases when the pressure loss is less than. 10 per cent of the initial pressure. When the loss in head is high, the formula to be used for gases is i Pi* - Pi* flV' pi* gd P&i .. . (gy which may be rearranged to give the loss in> pressure Pressure Loss In Non-Circular Pipes The formulas for flow in pipes are based upon the use of pipes of circular cross-section. The formulas may be used with conduits of other shapes, and in conduits riot flowing full, when the flow is turbulent, by using the hydraulic radius, i?H, which is really a' ratio: ^ ________area of cross-section wetted perimeter of cross-section (11) Table 1. Values of e/d for Different Kinds of Pipe . Type of pipe Smooth drawn tubing______________________ --............... Commercial steel or. wrought iron..................... .......................... Asphalted cast-iron.___________ _______ ____________ Galvanized iron..'............................................................. Cast-iron,,.,,,,.;_.J........................... .............1........ Wood stave...... ................................................. ............. Concrete......... .................................................. '---- -------Piveted steel....... ................................................... :......... e/d 0.000005 0.00015 . 0.0004 0.0005 0.00085 0.0006 to 0.003 0:001 to 0.01 0.003 to 0i03 Fluid Flout 79 For instance, in a square duct, I ft on a side, handling air, the hydraulic radius is or 0.25. If the same duct is handling water, flowing 9 in. deep, the hydraulic radius is 0.75/2.5 or 0.30. Note in this latter case that the wetted perimeter does not include the distance across the free surface. In the case of a round pipe Ra =^/^ = -~ord = 4Ra (12) Substituting Equation 12 in Equation 6, NRe=i^ P and in the flow Equation 5, hi = fly* SgRn and finally in the compressible fluid flow Equation 10, (13) . (14) pi -- pi = pi flVi* ] ig'Rll flFlJ (15) Equations 13, 14, and 15^ may be used to compute the flow in pipes arid ducts of non-circular section and in any type of conduit not flowing full. They should not be used when the flow is laminar. FLOW OF COMPRESSIBLE FLUIDS The energy equation for the flow of compressible fluids, as represented by the gases, is derived from Equation 1. Assuming that no heat is transferred to the fluid, that no work is done, and that there is no differ ence in elevation, Equation 1 becomes V,* p * -gj + Jui + P`.i:i = -gj- Ju, }- p.1, (16) or, after rearrangement, ... IV -- F,! -----2^----- = Pi*}-- Ptt + J(i -- i) (17) Since internal energy, is dependent only on temperature, where , ' ui - ? = cv{Ti - T,) (18) Cv =_the specific Keat of the gas at constant volume. Ti and I\ -- the temperatures in Fahrenheit degrees at points 1 and 2, respectively. Substituting Equation 18 in Equation 17, Now V' - IV 2g =* piii -- pi!* -f- Jcv(Ti -- Ti) R Cv T Ah -1) (19)' (20)