## Pipe - X - Pipe

UNDER CONSTRUCTION

This simulation is meant to demonstrate aspects of fluid dynamics. A summary of this system and its governing equations may be found below the simulation. Mouse-over each input to see a description of that option or variable. You may click on the units to change to units you prefer. Click on a variable symbol or double click in a textbox to attempt to determine an unknown.

'); top.consoleRef.document.close(); } if (iscsv && document.getElementById("controls_download")){ document.getElementById("controls_download").href="data:text/plain;charset=utf-8,"+escape(rText); } } function submitAnswers(){//turn in the answers document.getElementById('hiddenTrackData').value=trackdata; document.getElementById('options').value=options_txt; document.getElementById('for_credit').value=for_credit; for (var k in vars) { if (document.getElementById('hid='+k)){ document.getElementById('hid='+k).value=vars[k]['x'];//put answers into the hidden form fields } if (k==thequestion) {//the unknown that is being solved for document.getElementById('thequestion').value+=k+',';//put answers into the hidden form fields } if (vars[k]['isUnknown']) {//an unknown that may not be the solution document.getElementById('unknowns').value+=k+',';//put answers into the hidden form fields } } document.forms["Applet_Form"].submit();//and submit }

Fluid Flow Through Various Pipes & Elements

University of Utah - Department of Chemical Engineering
by Anthony Butterfield

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 ρ kg/m3g/cm3g/mlkg/Llb/ft3lb/gal μ Pa·skgf·s/m2N·s/m2mN·s/m2dyne·s/cm2PEPPPTPkPcPmPfPaPg/cm·s Q m3/sgpmL/hin3/sin3/mingphm3/minL/minL / s P1 PaatmbarcmHgcmH2Odyn/cm2ftHgftH2OinHginH2OkPaMPambarmmHgmmH2Olbf/ft2lbf/in2torr
 P2 PaatmbarcmHgcmH2Odyn/cm2ftHgftH2OinHginH2OkPaMPambarmmHgmmH2Olbf/ft2lbf/in2torr
 P3 PaatmbarcmHgcmH2Odyn/cm2ftHgftH2OinHginH2OkPaMPambarmmHgmmH2Olbf/ft2lbf/in2torr
 ReA fA
 ReB fB

#### Description of Governing Equations

In general, this simulation the pressure at Point 1 (P1) given a set volumetric flowrate (Q) and all the physical properties of the various elements, or it calculates the flowrate given the pressure drop. Iit's as though the pump is set to deliver a constant flowrate or head of pressure at Point 1. If you alter the value for Q, then P1 will be calculated and vice-versa.

The fluid's path always starts and ends with a pipe (you can effectively remove a pipe by making its length zero). Between pipe you can switch out common fluid dynamic elements. Click on a new element to place it between Pipe A and B. Values you can change are in a textbox with a white background; values that you cannot change (because they are dependent on other physical constants) have a grey background.

Governing equations for each element may be found in most any introductory fluids text book; equations that may be specific to this simulation are given below.

Pipes: The Fanning friction factor for the flow through a pipe is calculated using the following fit to the Moody diagram:

$f=0.001375\left[ 1+{ \left( 2e5\frac { \varepsilon }{ D } +\frac { 1e6 }{ Re } \right) }^{ \sfrac { 1 }{ 3 } } \right]$

Packed Bed: The Ergun equation is used to determine the pressure drop.

Sudden contractions or expansions when going from one element to the next, and lossess due to fittings are neglected in these calculations.