Frictional losses in hydraulic pipelines

Reynolds No.

where v = fluid velocity, D = pipe inside diameter, ρ = fluid density, and µ = absolute viscosity of the fluidand µ absolute viscosity of the fluid.

If NR is less than 2000, the flow is laminar.If NR is greater than 4000, the flow is turbulent.Reynolds numbers between 2000 and 4000 cover a critical zone

between laminar and turbulent flow. It is not possible to predict thetype of flow that will exist within the critical zone. Thus if NR lies inyp R

the critical zone, turbulent flow should be assumed.

Si t b l t fl lt i t l h d li tSince turbulent flow results in greater losses, hydraulic systemsshould normally be designed to operate in the laminar flow region.

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If turbulent flow is allowed to exist, higher fluid temperatures will, g poccur due to greater frictional energy losses. Therefore, turbulentflow systems suffering from excessive fluid temperatures can bei ed b i e i the i e di ete t e t bli h l i flimproved by increasing the pipe diameter to establish laminar flow.

Friction is the main cause of energy losses in fluid power systems.The result is a loss of potential energy in the system, and this showsup as a loss in pressure or head.

The head loss (HL) in a system actually consists of two components:1. Losses in pipes2. Losses in valves and fittings

Head losses in pipes can be found by using Darcy's equation:Head losses in pipes can be found by using Darcy s equation:

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Darcy's equation can be used to calculate the head loss due tofriction in pipes for both laminar and turbulent flow. The differencebetween the two lies in the evaluation of the friction factor f Forbetween the two lies in the evaluation of the friction factor f. Forlaminar flow:

To determine the value of the friction factor for use in Darcy,sequation, we use Moody diagram. It gives values of friction factoras a function of Reynolds number for a given value of relativeas a function of Reynolds number for a given value of relativeroughness.

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Head losses in valves and fittings are proportional to the square ofg p p qthe velocity of the fluid:

The constant of proportionality (K) is called the K factor (also calledloss coefficient) of the valve or fitting. Typical K-factor values forseveral common types of valves and fittings are:

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Pressure drop versus flow ratep

For some fluid power valves, indditi t if i K f taddition to specifying K factors,

empirical curves of pressuredrop versus flow rate are givenp gby the valve manufacturer. Thus,if the flow rate through the valveis known the pressure drop canis known, the pressure drop canbe determined by referring to thecurve. This is normally done fordirectional control valves andalso for flow control valves forvarious opening positionsvarious opening positions.

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Equivalent lengthWe can find a length of pipe that for the same flow rate wouldWe c d e g o p pe o e s e ow e wou dproduce the same head loss as a valve or fitting. This length of pipe,which is called the equivalent length of a valve or fitting, can bef d b ti th h d l th l fitti d thfound by equating the head losses across the valve or fitting and thepipe:

where L is the equivalent length of a valve or fitting whose K factorwhere Le is the equivalent length of a valve or fitting whose K factoris K. Note that K and f are both dimensionless. Therefore, Le and Dwill have the same dimensions. 6

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