Fluid dynamics

Moody chart

1. Moody’s Chart

2. Group members

3. History In 1939, Cyril F. Colebrook combined the available data for transition and turbulent flow in smooth as well as rough pipes into the Colebrook equation: In 1942, the American engineer Hunter Rouse verified Colebrook’s equation and produced a graphical plot of f.

4. In 1944, Lewis F. Moody redrew Rouse’s diagram into the form commonly used today, called Moody chart Performers 10,000 experiment. It is no way to find a mathematical closed form for friction factor by theoretical analysis; therefore, all the available results are obtained from painstaking experiments. Plotted the Chart b/w Darcy – Weisbach friction factor fD against Reynolds number Re for various values of relative roughness ε / D. History

5. LAMINAR AND TURBULENT FLOWS Laminar flow : characterized by smooth streamlines and highly ordered motion. Turbulent flow : characterized by velocity fluctuations and highly disordered motion. The transition from laminar to turbulent flow does not occur suddenly; rather, it occurs over some region in which the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent.

6. Reynolds Number British engineer Osborne Reynolds (1842–1912) discovered that the flow regime depends mainly on the ratio of inertial forces to viscous forces in the fluid. The ratio is called the Reynolds number and is expressed for internal flow in a circular pipe as

7. Reynolds Number For flow through noncircular pipes, the Reynolds number is based on the hydraulic diameter Dh defined as Ac = cross-section area P = wetted perimeter The transition from laminar to turbulent flow also depends on the degree of disturbance of the flow by surface roughness, pipe vibrations, and fluctuations in the flow.

8. THE ENTRANCE REGION

9. Pressure Drop The pressure drop represents the pressure loss ∆PL In practice, it is found convenient to express the pressure loss for all types of fully developed internal flows as It is also called the Darcy–Weisbach friction facto r, named after the Frenchman Henry Darcy (1803–1858) and the German Julius Weisbach (1806–1871)

10. The Moody Chart

11. For laminar flow, the friction factor decreases with increasing Reynolds number, and it is independent of surface roughness The friction factor is a minimum for a smooth pipe and increases with roughness The data in the transition region are the least reliable.

12. Observations from the Moody chart In the transition region, at small relative roughness's, the friction factor increases and approaches the value for smooth pipes. At very large Reynolds numbers, the friction factor curves corresponding to specified relative roughness curves are nearly horizontal, and thus the friction factors are independent of the Reynolds number. The flow in that region is called fully rough turbulent flow or just fully rough flow

13. Variables: roughness Roughness is important in the viscous sub-layer in turbulent flows, if it protrudes sufficiently in this layer . Then range of roughness for validity of this analysis is for: Then, the dimensionless groups are the following: The viscous layer in laminar flow is so large, that small roughness does not play a role.

14. Dimensional Analysis of Pipe Flow For fully developed pipe flow in a horizontal pipe: a’s account for non-uniform velocity profiles Darcy-Weisbach Equation

15. The Moody Chart Basically for turbulent flow When solving many fluid dynamics problems, be it steady state or transient, the Darcy-Weisbach friction factor, f, is necessary. In circular pipes this factor can be solved directly with the Swamee-Jain equation, as well as others, however most of these equations are complicated, and become cumbersome when iteration is necessary. Therefore, it is often effective to solve for this friction factor using the Moody Chart.

16. Procedure to read the Moody’s Chart C alculate the Reynolds Number Compute relative roughness T he wall roughness may be zero, making the relative roughness zero, this does NOT mean that the friction factor will be zero. Find the line referring to your relative roughness on the right side of the diagram Follow this line to the left as it curves up until to reach the vertical line corresponding to your flow's Reynolds Number.

17. Mark this point on the Chart. Using a straight edge, follow the point straight left, parallel to the x axis, until you reach the far left side of the chart Read off the corresponding friction factor Calculate the energy losses knowing the friction factor. Calculate a new velocity and Reynolds Number. Procedure to read the Moody’s Chart

18. Pumping power

19. Pumps A device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action Three groups: Direct lift Displacement Gravity pumps

20. Pumps Pump’s performance is described by the following parameters: Capacity Head Power Efficiency Net positive suction head Specific speed Capacity, Q, is the volume of water delivered per unit time by the pump (usually gpm )

21. Piping Networks Two general types of networks Pipes in series Volume flow rate is constant Head loss is the summation of parts Pipes in parallel Volume flow rate is the sum of the components Pressure loss across all branches is the same

22. Piping Networks and Pump Selection For parallel pipes, perform CV analysis between points A and B Piping Networks and Pump Selection

23. Pump Performance: power The power imparted into a fluid increases the energy of the fluid per unit volume Power to operate a pump is directly proportional to discharge head, specific gravity of the fluid (water), and is inversely proportional to pump efficiency Usually determined by brake horsepower ( BHP) BHP = power that must be applied to the shaft of the pump by a motor to turn the impeller and impart power to the water

24. Pumping Power Head is the net work done on a unit of water by the pump and is given by the following equation Hs = SL + DL + DD + hm + hf + ho + hv Hs = system head, SL = suction-side lift, DD = water source drawdown, hm = minor losses (as previous), hf = friction losses (as previous), ho = operating head pressure, and hv = velocity head (V2/2g) Suction and discharge static lifts are measured when the system is not operating DD, drawdown, is decline of the water surface elevation of the source water due to pumping (mainly for wells) DD, hm, hf, ho and hv all increase with increased pumping capacity, Q

25. Pump Performance: efficiency Ep = 100(WHP/BHP) = output/input E p never equals 100% due to energy losses such as friction in bearings around shaft, moving water against pump housing, etc Centrifugal pump efficiencies range from 25-85% If pump is incorrectly sized, E p is lower

26. Pump Performance: suction head Conditions on the suction side of a pump can impart limitations on pumping systems What is the elevation of the pump relative to the water source? Static suction lift (SL) = vertical distance from water surface to centerline of the pump SL is positive if pump is above water surface, negative if below Total suction head (Hs) = SL + friction losses + velocity head: H s = SL + (h m + h f ) + V 2 s /2g

27. Pump Performance Curves Report data on a pump relevant to head, efficiency, power requirements, and net positive suction head to capacity Each pump is unique dependent upon its geometry and dimensions of the impeller and casing Reported as an average or as the poorest performance

28. Characteristic Pump Curves Head  as capacity  Efficiency  as capacity , up to a point BHP  as capacity , also up to a point REM: BHP = 100QHS/E p 3,960

29. Pump and systems curves

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