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Pipe Pressure Loss Calculator

Wall drag and changes in height lead to pressure drops in pipe fluid flow.

To calculate the pressure drop and flowrates in a section of uniform pipe running from Point

A to Point B, enter the parameters below. The pipe is assumed to be relatively straight (no

sharp bends), such that changes in pressure are due mostly to elevation changes and wall

friction. (The default calculation is for a smooth horizontal pipe carrying water, with answers

rounded to 3 significant figures.)

Note that a positive zmeans that B is higher than A, whereas a negative zmeans that B is

lower than A.

Inputs

Pressure at A (absolute): 100

Average fluid velocity in pipe, V: 1

Pipe diameter, D: 10

Pipe relative roughness, e/D:

0

Pipe length from A to B, L: 50

Elevation gain from A to B, z: 0

Fluid density, : 1

Fluid viscosity (dynamic), : 1

Answers

Reynolds Number, R: 1.00 105

Friction Factor, f: 0.0180

Pressure at B: 95.5 kPa

Pressure Drop: 4.50 kPa

Volume Flowrate: 7.85 l/s

Mass Flowrate: 7.85 kg/s

Select desired output units fornext calculation.

Calculate Again Default Values

Hint: To Calculate a Flowrate

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You can solve for flowrate from a known pressure drop using this calculator (insteadof solving for a pressure drop from a known flowrate or velocity).

Proceed by guessing the velocity and inspecting the calculated pressure drop. Refine your

velocity guess until the calculated pressure drop matches your data.

Equations used in the Calculation

Changes to inviscid,incompressible flow moving from Point A to Point B along a pipeare described by Bernoulli'sequation,

wherep is the pressure, Vis the average fluid velocity, is the fluid density, zis the

pipe elevation above some datum, and gis the gravity acceleration constant.

Bernoulli's equation states that the total head h along a streamline (parameterized byx)

remains constant. This means that velocity head can be converted into gravity head and/or

pressure head (or vice-versa), such that the total head h stays constant. No energy is lost in

such a flow.

For real viscous fluids, mechanical energy is converted into heat (in the viscous boundarylayer along the pipe walls) and is lost from the flow. Therefore one cannot use Bernoulli's

principle of conserved head (or energy) to calculate flow parameters. Still, one can keep track

of this lost head by introducing another term (called viscous head) into Bernoulli's equation to

get,

where D is the pipe diameter. As the flow moves down the pipe, viscous head slowlyaccumulates taking available head away from the pressure, gravity, and velocityheads. Still, the total head h (or energy) remains constant.

For pipe flow, we assume that the pipe diameterD stays constant. By continuity, we then

know that the fluid velocity Vstays constant along the pipe. WithD and Vconstant we can

integrate the viscous head equation and solve for the pressure at Point B,

where L is the pipe length between points A and B, and zis the change in pipe

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elevation (zB - zA). Note that zwill be negative if the pipe at B is lower than at A.

The viscous head term is scaled by the pipe friction factor f. In general,fdepends on the

Reynolds NumberR of the pipe flow, and the relative roughness e/D of the pipe wall,

The roughness measure e is the average size of the bumps on the pipe wall. Therelative roughness e/D is therefore the size of the bumps compared to the diameter ofthe pipe. For commercial pipes this is usually a very small number. Note that perfectlysmooth pipes would have a roughness of zero.

Forlaminarflow (R < 2000 in pipes),fcan be deduced analytically. The answer is,

Forturbulentflow (R> 3000 in pipes), fis determined from experimental curve fits.One such fit is provided by Colebrook,

The solutions to this equation plotted versus Rmake up the popular Moody Chart forpipe flow,

The calculatorabove first computes the Reynolds Number for the flow. It then

computes the friction factorfby direct substitution (if laminar; the calculator uses thecondition that R< 3000 for this determination) or by iteration using Newton-Raphson

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(if turbulent). The pressure drop is then calculated using the viscous head equationabove. Note that the uncertainties behind the experimental curve fits place at least a10% uncertainty on the deduced pressure drops. The engineer should be aware ofthis when making calculations.

Calculator

This calculator computes the Reynolds Number given the flow characteristics askedfor below. It outputs the flow type you can expect (laminar, transitional, orturbulent) based on the Reynolds Number result.

Think of the Characteristic Distance as the distance from the leading edge (where the fluid

first makes contact) for flow over a plate, or as the pipe diameter for flow inside a pipe.

InputsFree-stream fluid velocity, V:

1

Characteristic distance (or pipe diameter), D: 10

Fluid density, : 1

Fluid viscosity (dynamic), : 1

Answers

Reynolds Number, R: 1.00 105

Calculate Again Default Values

Plate flow is transitioning to turbulent at a distance D from the leading edge.

Pipe flow is fully turbulent in a pipe of diameterD.

Equation Behind the Calculator

The Reynolds Number is found from the equation,

barotropic A barotropic fluid is one whose pressure and density are related by anequation of state that does not contain the temperature as a dependent variable.

Mathematically, the equation of state can be expressed asp =p() or = (p).

compressible A fluid flow is compressible if its density changes appreciably(typically by a few percent) within the domain of interest. Typically, this will occur

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when the fluid velocity exceeds Mach 0.3. Hence, low velocity flows (both gas andliquids) behave incompressibly.

density, The mass of fluid per unit volume. For a compressible fluid flow, thedensity can vary from place to place.

incompressible An incompressible fluid is one whose density is constanteverywhere. All fluids behave incompressibly (to within 5%) when their maximumvelocities are below Mach 0.3.inviscid Not viscous.

irrotational An irrotational fluid flow is one whose streamlines never loop back onthemselves. Typically, only inviscid fluids can be irrotational. Of course, a uniformviscid fluid flow without boundaries is also irrotational, but this is a special (andboring!) case.

Laminar (non-turbulent) An organized flow field that can be described withstreamlines. In order for laminar flow to be permissible, the viscous stresses mustdominate over the fluid inertia stresses.

Mach Mach number is the relative velocity of a fluid compared to its sonic velocity.Mach numbers less than 1 correspond to sub-sonic velocities, and Mach numbers >1 correspond to super-sonic velocities.

Newtonian A Newtonian fluid is a viscous fluid whose shear stresses are a linear

function of the fluid strain rate. Mathematically, this can be expressed as: ij =

Kijqp*Dpq, where ij is the shear stress component, and Dpq are fluid strain ratecomponents.perfect A perfect fluid is defined as a fluid with zero viscosity (i.e. inviscid).

rotational A rotational fluid flow can contain streamlines that loop back onthemselves. Hence, fluid particles following such streamlines will travel along closedpaths. Bounded (and hence nonuniform) viscous fluids exhibit rotational flow,typically within their boundary layers. Since all real fluids are viscous to someamount, all real fluids exhibit a level of rotational flow somewhere in their domain.Regions of rotational flow correspond to the regions of viscous losses in a fluid.Inviscid fluid flows can also be rotational, but these are special nonphysical cases.

For an inviscid fluid flow to be rotational, it must be set up that way by initialconditions. The amount of rotation (called the velocity circulation) in an inviscid fluidflow is conserved, provided that the fluid is also barotropic and subject only toconservative body forces. This conservation is known as Kelvin's Theorem ofconstant circulation.

Stokesian A Stokesian (or non-Newtonian) fluid is a viscous fluid whose shearstresses are a non-linear function of the fluid strain rate. streamline A path in asteady flow field along which a given fluid particle travels.

turbulent A flow field that cannot be described with streamlines in the absolute

sense. However, time-averaged streamlines can be defined to describe the average

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behavior of the flow. In turbulent flow, the inertia stresses dominate over the viscousstresses, leading to small-scale chaotic behavior in the fluid motion.

viscosity, A fluid property that relates the magnitude of fluid shear stresses to thefluid strain rate, or more simply, to the spatial rate of change in the fluid velocity field.

Mathematically, this is expressed as: = *(dV/dy), where is the shear stress in thesame direction as the fluid velocity V, and yis a direction perpendicular to the fluidvelocity direction.