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CE 230-Engineering Fluid Mechanics Lecture # 29-30 Turbulent flow in circular pipes Head loss for turbulent flow Difficult to develop velocity distribution Newton’s viscosity law does not apply, instead: du u ' v ' la min ar turbulant dy Head loss formula, Turbulent flow Avoiding detail a formula that is widely used is Darcy-Weisbach equation: 2 LV hf f D 2g Where : f friction factor function of Re and material type and size Other variables are well known by now Factors affecting f Smooth pipes only Re is important Rough pipes Re as well as ks/D Fully turbulent Re is not important See Moody chart or equations Rough pipes We can idealize the roughness in pipes using mean values which are reported for different materials as ks shown below Classes of problems handled Given size and type of pipe and Q find head loss. Given size and type of pipe and head loss find Q. Given type of pipe, Q and head loss find size. Type one problem =0.12/200 V= Q/A=1.6 m/s Re=1000(1.6)(.2)/0.001=320000 From Moody Chart f=0.019 Type one problems Example 10.5: If the head loss per kilometer for a 30-cm diameter asphalt cast iron pipe is 12.2 m, estimate Q. Example 10.6 Estimate Q through the 50 cm diameter steel pipe.. Type three problem Example 10.6: What size of asphalt cast iron pipe is required to carry Q=3cfs with a head loss of 4 ft per 1000 ft of pipe?