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Pipe Sizing Basics. Major & Minor Losses Under Supervision of: Prof . Dr. Mahmoud Fouad By students : Mahmoud Bakr 533 Mohammed Abdullah 511 Moaz Emad 619 Mohammed Nabil Abbas 525. Applications . How big does the pipe have to be to carry a flow of x m 3 /s?.

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pipe sizing basics

Pipe Sizing Basics

Major & Minor Losses

Under Supervision of:

Prof. Dr. Mahmoud Fouad

By students:

Mahmoud Bakr 533 Mohammed Abdullah 511

Moaz Emad 619 Mohammed Nabil Abbas 525

bernoulli s equation
Bernoulli's Equation
  • The basic approach to all piping systems is to write the Bernoulli equation between two points, connected by a streamline, where the conditions are known. For example, between the surface of a reservoir and a pipe outlet.
  • The total head at point 0 must match with the total head at point 1, adjusted for any increase in head due to pumps, losses due to pipe friction and so-called "minor losses" due to entries, exits, fittings, etc. Pump head developed is generally a function of the flow through the system
friction losses in pipes
Friction Losses in Pipes
  • Friction losses are a complex function of the system geometry, the fluid properties and the flow rate in the system. By observation, the head loss is roughly proportional to the square of the flow rate in most engineering flows (fully developed, turbulent pipe flow). This observation leads to the Darcy-Weisbach equation for head loss due to friction
slide7

which defines the friction factor, f. f is insensitive to moderate changes in the flow and is constant for fully turbulent flow. Thus, it is often useful to estimate the relationship as the head being directly proportional to the square of the flow rate to simplify calculations.

slide8

Reynolds Number is the fundamental dimensionless group in viscous flow. Velocity times Length Scale divided by Kinematic Viscosity. Relative Roughness relates the height of a typical roughness element to the scale of the flow, represented by the pipe diameter, D. Pipe Cross-section is important, as deviations from circular cross-section will cause secondary flows that increase the pressure drop. Non-circular pipes and ducts are generally treated by using the hydraulic diameter, in place of the diameter and treating the pipe as if it were round

slide9

For laminar flow, the head loss is proportional to velocity rather than velocity squared, thus the friction factor is inversely proportional to velocity

turbulent flow
Turbulent flow
  • For turbulent flow, Colebrook (1939) found an implicit correlation for the friction factor in round pipes. This correlation converges well in few iterations. Convergence can be optimized by slight under-relaxation.
slide11

The familiar Moody Diagram is a log-log plot of the Colebrook correlation on axes of friction factor and Reynolds number, combined with the f=64/Re result from laminar flow. The plot below was produced in an Excel spreadsheet

pipe roughness

Must be dimensionless!

Pipe roughness

pipe material

pipe roughness

(mm)

glass, drawn brass, copper

0.0015

commercial steel or wrought iron

0.045

asphalted cast iron

0.12

galvanized iron

0.15

cast iron

0.26

concrete

0.18-0.6

rivet steel

0.9-9.0

corrugated metal

45

0.12

PVC

calculating head loss for a known flow
Calculating Head Loss for a Known Flow
  • From Q and piping determine Reynolds Number, relative roughness and thus the friction factor. Substitute into the Darcy-Weisbach equation to obtain head loss for the given flow. Substitute into the Bernoulli equation to find the necessary elevation or pump head
calculating flow for a known head
Calculating Flow for a Known Head

Obtain the allowable head loss from the Bernoulli equation, then start by guessing a friction factor. (0.02 is a good guess if you have nothing better.) Calculate the velocity from the Darcy-Weisbach equation. From this velocity and the piping characteristics, calculate Reynolds Number, relative roughness and thus friction factor.

Repeat the calculation with the new friction factor until sufficient convergence is obtained. Q = VA

minor losses
"Minor Losses"

Although they often account for a major portion of the head loss, especially in process piping, the additional losses due to entries and exits, fittings and valves are traditionally referred to as minor losses. These losses represent additional energy dissipation in the flow, usually caused by secondary flows induced by curvature or recirculation. The minor losses are any head loss present in addition to the head loss for the same length of straight pipe.

Like pipe friction, these losses are roughly proportional to the square of the flow rate. Defining K, the loss coefficient, by

slide17

. K is the sum of all of the loss coefficients in the length of pipe, each contributing to the overall head loss

  • Although K appears to be a constant coefficient, it varies with different flow conditions

Factors affecting the value of K include :

the exact geometry of the component,.

the flow Reynolds number , etc .

some types of minor losses head loss due to gradual expansion diffuser

0.8

0.7

0.6

0.5

KE

0.4

0.3

0.2

0.1

0

0

20

40

60

80

diffusor angle ()

Some types of minor lossesHead Loss due to Gradual Expansion (Diffuser)
sudden contraction
Sudden Contraction
  • losses are reduced with a gradual contraction

V2

V1

flow separation

sudden contraction1

1

0.95

0.9

0.85

Cc

0.8

0.75

0.7

0.65

0.6

0

0.2

0.4

0.6

0.8

1

A2/A1

Sudden Contraction
entrance losses
Entrance Losses

Losses can be reduced by accelerating the flow gradually and eliminating the

vena contracta

head loss in bends
Head Loss in Bends

High pressure

  • Head loss is a function of the ratio of the bend radius to the pipe diameter (R/D)
  • Velocity distribution returns to normal several pipe diameters downstream

Possible separation from wall

R

D

Low pressure

Kb varies from 0.6 - 0.9

head loss in valves
Head Loss in Valves
  • Function of valve type and valve position
  • The complex flow path through valves can result in high head loss (of course, one of the purposes of a valve is to create head loss when it is not fully open)
solution techniques
Solution Techniques
  • Neglect minor losses
  • Equivalent pipe lengths
  • Iterative Techniques
  • Simultaneous Equations
  • Pipe Network Software
iterative techniques for d and q given total head loss
Iterative Techniques for D and Q (given total head loss)
  • Assume all head loss is major head loss.
  • Calculate D or Q using Swamee-Jain equations
  • Calculate minor losses
  • Find new major losses by subtracting minor losses from total head loss
solution technique head loss
Solution Technique: Head Loss
  • Can be solved directly
solution technique discharge or pipe diameter
Solution Technique:Discharge or Pipe Diameter
  • Iterative technique
  • Set up simultaneous equations in Excel

Use goal seek or Solver to find discharge that makes the calculated head loss equal the given head loss.

example minor and major losses
Example: Minor and Major Losses
  • Find the maximum dependable flow between the reservoirs for a water temperature range of 4ºC to 20ºC.

25 m elevation difference in reservoir water levels

Water

Reentrant pipes at reservoirs

Standard elbows

2500 m of 8” PVC pipe

Sudden contraction

Gate valve wide open

1500 m of 6” PVC pipe

directions
Directions
  • Assume fully turbulent (rough pipe law)
    • find f from Moody (or from von Karman)
  • Find total head loss
  • Solve for Q using symbols (must include minor losses) (no iteration required)
  • Obtain values for minor losses from notes or text
example continued
Example (Continued)
  • What are the Reynolds number in the two pipes?
  • Where are we on the Moody Diagram?
  • What value of K would the valve have to produce to reduce the discharge by 50%?
  • What is the effect of temperature?
  • Why is the effect of temperature so small?
example continued1
Example (Continued)
  • Were the minor losses negligible?
  • Accuracy of head loss calculations?
  • What happens if the roughness increases by a factor of 10?
  • If you needed to increase the flow by 30% what could you do?
  • Suppose I changed 6” pipe, what is minimum diameter needed?