Solution of Pipe Flow Problems. Class 21 Fluid Mechanics. Types of Pipe Flow Problems 4/6/2011. Energy Equation. Tuesday, April 5.

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1 4/6/ Class Fluid Mechanics Energy Equation Tuesday, April 5 Types of Pipe Flow Problems Single pipes Determine pressure drop or head loss Determine flow rate or average velocity Pipe diameter Multiple pipe systems Series Parallel Single Path Find p for a given L, D, and Q Use energy equation directly Find L for a given p, D, and Q Use energy equation directly

2 4/6/ Assume a car s exhaust system can be approximated as 4 ft. of.5 ft diameter castiron pipe with the equivalent of six 9 o flanged elbows and a muffler. The muffler acts as a resistor with a loss coefficient of KL = 8.5. Determine the pressure at the beginning of the exhaust system if the flowrate is. cfs, the temperature is 5 o F and the exhaust has the same properties as air. Assume a car s exhaust system can be approximated as 4 ft. of.5 ft diameter castiron pipe with the equivalent of six 9 o flanged elbows and a muffler. The muffler acts as a resistor with a loss coefficient of KL = 8.5. Determine the pressure at the beginning of the exhaust system if the flowrate is. cfs, the temperature is 5 o F and the exhaust has the same properties as air. ) Simplify energy equation. a) b) c) d) ρv p p = KL l ρvρ V p p = f + KL D ( V V ) p p = ρ + K l ρv p = f + KL D L ρv video ) Determine flow regime. Assume a car s exhaust system can be approximated as 4 ft. of.5 ft diameter castiron pipe with the equivalent of six 9 o flanged elbows and a muffler. The muffler acts as a resistor with a loss coefficient of K L = 8.5. Determine the pressure at the beginning of the exhaust system if the flowrate is. cfs, the temperature is 5 o F and the exhaust has the same properties as air. ) Find friction factor.

3 4/6/ Assume a car s exhaust system can be approximated as 4 ft. of.5 ft diameter castiron pipe with the equivalent of six 9 o flanged elbows and a muffler. The muffler acts as a resistor with a loss coefficient of K L = 8.5. Determine the pressure at the beginning of the exhaust system if the flowrate is. cfs, the temperature is 5 o F and the exhaust has the same properties as air. 4) Sum minor losses (for K L ) Assume a car s exhaust system can be approximated as 4 ft. of.5 ft diameter castiron pipe with the equivalent of six 9 o flanged elbows and a muffler. The muffler acts as a resistor with a loss coefficient of K L = 8.5. Determine the pressure at the beginning of the exhaust system if the flowrate is. cfs, the temperature is 5 o F and the exhaust has the same properties as air. 5) Solve for P. Single Path (Continued) Find Q for a given p, L, and D. Manually iterate energy equation and friction factor formula to find V (or Q), or. Directly solve, simultaneously, energy equation and friction fiti factor formula using (for example) l) Excel Find D for a given p, L, and Q. Manually iterate energy equation and friction factor formula to find D, or. Directly solve, simultaneously, energy equation and friction factor formula using (for example) Excel A certain process requires. cfs of water to be delivered at a pressure of psi This water comes from a large diameter supply main in which the pressure remains at 6 psi. if the galvanized iron pipe connecting the two locations is ft long and contains six threaded 9o elbows, determine the pipe diameter. Neglect elevation differences. ) Simplify energy equation. ) Write it in terms of D. ) Write Re in terms of D. 4) Write ε/d in terms of D.

4 4/6/ A certain process requires. cfs of water to be delivered at a pressure of psi This water comes from a large diameter supply main in which the pressure remains at 6 psi. if the galvanized iron pipe connecting the two locations is ft long and contains six threaded 9o elbows, determine the pipe diameter. Neglect elevation differences. ) Guess a D. ) Calculate f, Re, ε/d. ) Use Re, ε/d for Moody to find f. 4

5 4/6/ Multiple Path Systems Example: Multiple Path Systems Solve each branch as for single path Analogy: circuits = Q 5Q ft /s. Friction factor in each pipe is., and minor losses and gravity are Energy balance between and : 5

6 4/6/ = Q 5Q ft /s. Friction factor in each pipe is., and minor losses and gravity are = Q 5Q ft /s. Friction factor in each pipe is., and minor losses and gravity are Energy balance between and, and and : Set them equal to each other to solve for V = f(v ) = Q 5Q ft /s. Friction factor in each pipe is., and minor losses and gravity are = Q 5Q ft /s. Friction factor in each pipe is., and minor losses and gravity are Solve for Q = f(q ) and write Q as f(q ): h p V = ( + f g V = 5.9Q Q =.488Q put everything together Q 4.9Q 45 = l ) = Q 54Q D 6