pfit

Other Friction Losses: 

Other Friction Losses Valves and Fittings

Goals: 

Goals Calculate frictional losses in a system containing valves, fittings, and sudden expansions and contractions Express frictional losses in terms of velocity head Assess relative contributions of different sources to total viscous dissipation

Sudden Expansion: 

Sudden Expansion Frictional losses occur as result of turbulence generated immediately downstream of the expansion

Sudden Expansion: 

Sudden Expansion Assume Ke is the expansion loss coefficient which we will attempt to describe in terms of flow properties.

Sudden ExpansionMass Balance: 

Sudden Expansion Mass Balance

Sudden ExpansionMomentum Balance: 

Sudden Expansion Momentum Balance 0 0 Assume turbulent: b1 = b2 = 1 Replaced Sa with Sb because pa is at the point of expansion.

Momentum Balance: 

Momentum Balance

Mechanical Energy Balance: 

Mechanical Energy Balance Assume turbulent: a1 = a2 = 1 0 0

Combining: 

Combining

Final Result: 

Final Result Recall Mass Balance Result: Notes: Velocity head is based on smaller cross section What if flow becomes laminar in large pipe?

For Tank Filling: 

For Tank Filling Sa Va Sb

Sudden Contractions: 

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.

Sudden Contraction: 

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 hfc is usually neglected Turbulent (empirical): Note: Calculations again based on small cross section.

Tank Emptying: 

Tank Emptying Sb Vb Sa

Velocity Heads: 

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.

Alternate Method: 

Alternate Method The previous equation can be manipulated to change the Kf 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.

Example: 

Example 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%. Pa = 0 psig