# Information the Might be Useful for the Exam Information the Might be Useful for the Exam Unit conversions and physical properties of water 1 ft3 = 7.48 gal; 1 cfs = 448.8 gpm; 20oC: 60oF: 1 hp = 550 ft-lb/s r = 998.2 kg/m3 g = 9.79 kN/m3 n = 1.00x10-6 m2/s m = 1.00x10-3 N-s/m2 pvap = 2.34 kPa = 0.00234 atm r = 1.94 slug/ft3 g = 62.4 lb/ft3 n = 1.21x10-5 ft2/s m = 2.34x10-5 lb-s/ft2 pvap = 0.256 lb/ft2 Equations characterizing friction and headloss in turbulent pipe flow: D 1 2.71 - 2 log

f 3.7 Re f D 1.11 6.9 1 - 1.8log Re f 3.7 Colebrook Eqn. Haaland Eqn. D 2.51n 2 gDhL V - 2

log l D 3.7 l 2 gDhL Hazen-Williams Eqn for SI units (for BG units, replace 0.849 by 1.318, 10.7 by 4.73, and 0.278 by 0.432): V 0.849CHW R 0.63 h hL l

Q1.85 1 hL 10.7l 4.87 1.85 D CHW 0.54 Q 0.278 D 2.63 S 0.54CHW Headloss equations for equivalent pipes: hL , series K i Q n hL , parallel K - 1/ n - n i Iterative corrections for analysis of pipe networks: h L ,i ,0

Q j ,0 - loop hL ,i ,0 n loop Qi ,0 h j ,0 - n Qi ,0 node Qi ,0 node hL ,i ,0 n Qtot Net Positive Suction Head Available (NPSHA): The absolute dynamic head in the pump inlet in excess of the vapor pressure Vs2 pvap

NPSH A g 2g g ps ,abs zsl ,max patm ,abs g - h L - pvap g

- NPSH R Some useful dimensionless groups for pump similitude: g TDH CH 2 2 D CP Pshaft 3 r D 5 Pf Pshaft To a good approximation, for geometrically similar pumps, all are functions of only CQ Q D.3

Some Basic Information Expected to be Known p2 V22 p1 V12 z2 z1 hpump - hturb g 2g g 2g l V2 hL f D 2g For a given pipe: f lam h L, f 64 Re ' Q hL klam

hL k full Q 2 turb V2 hL K minor 2g Aflow D 2 4 D R Rh Pwetted D 4 2 Pfluid gQh Explain some aspect of these diagrams. For example, why do the curves change as they do?; what would happen if a new pump or pipe were added to the system, or if an existing pump were replaced

with a similar one with a larger diameter?; etc. Typical Exam Questions Characterize a pipe equivalent to A, B, C, and D. If an equivalent pipe were identified, and a second pipe parallel to D were then installed, would the length of the equivalent pipe increase, decrease, or not change? Given initial guesses of Q and the values of K and n for hL=KQn in each pipe, what would be the correction to the flow in pipe BE? Sketch reasonable pump curves and system curves for the above network, for conditions where the upper reservoir is at its (1) highest and (2) lowest levels. CH

CH CP CP CQ If the conditions in a system with this fixed-speed pump changed so that CQ increased from 0.05 to 0.06, how much would the fluid power change, if at all?