CBE 150A – Transport Spring Semester 2014 Other Friction Losses Valves and Fittings

CBE 150A – Transport Spring Semester 2014 Goals Calculate frictional losses in a system containing valves, fittings, and sudden expansions and contractionsCalculate frictional losses in a system containing valves, fittings, and sudden expansions and contractions Express frictional losses in terms of velocity headExpress frictional losses in terms of velocity head Assess relative contributions of different sources to total viscous dissipationAssess relative contributions of different sources to total viscous dissipation

CBE 150A – Transport Spring Semester 2014 Sudden Expansion Frictional losses occur as result of turbulence generated immediately downstream of the expansion

CBE 150A – Transport Spring Semester 2014 Sudden Expansion Assume Ke is the expansion loss coefficient which we will attempt to describe in terms of flow properties.

CBE 150A – Transport Spring Semester 2014 Sudden Expansion Mass Balance

CBE 150A – Transport Spring Semester 2014 Sudden Expansion Momentum Balance 00 Assume turbulent:  1  2  Replaced S a with S b because p a is at the point of expansion.

CBE 150A – Transport Spring Semester 2014 Momentum Balance

CBE 150A – Transport Spring Semester 2014 Mechanical Energy Balance Assume turbulent:  1  2  00

CBE 150A – Transport Spring Semester 2014 Combining

CBE 150A – Transport Spring Semester 2014 Final Result Recall Mass Balance Result: Notes: Velocity head is based on smaller cross section What if flow becomes laminar in large pipe?

CBE 150A – Transport Spring Semester 2014 For Tank Filling SaSa VaVa SbSb

CBE 150A – Transport Spring Semester 2014 Sudden Contractions At sudden contractions, flow streamlines converge causing the downstream developed flow to have an area smaller than the downstream pipe diameter. This flow constriction is called the vena contracta. Viscous dissipation occurs in the vortices developed in this area.

CBE 150A – Transport Spring Semester 2014 Sudden Contraction Development of an expression for sudden contraction proceeds in much the same way as that for sudden expansion with the definition of a contraction coefficient. For laminar flow experimentally, Kc < 0.1 and h fc is usually neglected Turbulent (empirical): Note: Calculations again based on small cross section.

CBE 150A – Transport Spring Semester 2014 Tank Emptying SbSb VbVb SaSa

CBE 150A – Transport Spring Semester 2014 Velocity Heads The above expression shows that friction loss in a complicated flow system can be expressed as a number of velocity heads. It is a measure of momentum loss resulting from flow through the system. For instance in making a 90° turn all x- momentum is turned into y-momentum.

CBE 150A – Transport Spring Semester 2014 Alternate Method The previous equation can be manipulated to change the K f values into equivalent lengths of pipe (see attached table) of diameter D. When this method is used the equivalent lengths are add to the length of the actual pipe sections and the equation becomes. Note: The values in the table are L/D and must be multiplied by D to get equivalent lengths.

CBE 150A – Transport Spring Semester 2014

Example a e c Tank 1 L 2 =10 ft 5” Sch. 40 Steel P e = 30 psig Tank 2 d b L 2 =90 ft 4” Sch. 40 Steel ∆Z ab = -10 ft ∆Z bc = +0.5 ft ∆Z cd = +75 ft ∆Z de = +15 ft gate valve (open) Water is pumped at 250 gpm from tank 1 to tank 2 as shown. Calculate the required power input to the pump assuming a pump efficiency of 70%. P a = 0 psig

CBE 150A – Transport Spring Semester 2014

10 Minute Problem The Alaskan pipeline is 48 in. ID, 800 miles long and carries crude oil at a rate of 1.2 million bbl/day (1 bbl = 42 gallons). Assuming North Slope crude oil to be a Newtonian fluid with a viscosity of 25 cP and a specific gravity of 0.87, what total pumping horsepower is required to operate the pipeline ? The oil enters and leaves the pipeline at sea level and the line contains the equivalent of 150 – 90 degree elbows and 100 fully open gate valves. Assume inlet and discharge pressures are equal to 1 atm.