Determine velocity at a cross section of the pipe, Mechanical Engineering

Consider a fully developed laminar flow of a fluid through a 200 m long and 4 cm diameter horizontal and circular pipe. The density and the viscosity of the fluid are 1400 kg/m3 and 0.3073 kg/(m.s). The velocity profile at a cross section is given by u(r) = 8 [1 - (r/R)2] in m/s, where r is the axial distance from the center and R is the radius of the pipe. Determine the following:

(i)   the maximum velocity at a cross section of the pipe, umax

(ii)  the average velocity at a cross section of the pipe, Vavg

(iii) the volume flow rate, ý

(iv) Reynolds number, Re  of the flow

(v)  Friction factor, f

(vi) Head loss, hL

(vii)Pressure loss, DP

(viii) Pumping power required, ω

(ix)  For the same pumping power calculated above, the percent decrease of the flow rate if the pipe is inclined 15o upward (assume the head loss, hL calculated in part (vi) does not change)

Useful formulae:   f = 64/Re and  hL = f (L/D)(V2/2g)

Posted Date: 3/14/2013 3:00:51 AM | Location : United States

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