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Flow Through a PumpSamir KhanAdept Scientific plc
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>
A pipe receives water from a centrifugal pump. This worksheet will calculate the flowrate through the pipe.It also highlights several Maple 10 concepts.The ability to solve sets of equations iteratively.The use of document blocks to suppress the display of Maple code.The use of text boxes for the input of physical parameters.Push buttons to initiate calculation and display results.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
<Text-field style="Heading 1" layout="Heading 1">Governing Equations</Text-field>This worksheet collectively solves the following equations to find the fluid velocity in the exit piping, and hence the Reynolds number, the head produced by the pump and the volumetric flowrate.The Bernoulli Equation for the System'9.81*H=f*L/Dia*V^2/2';The Reynolds Number'Ren=Dia*V*rho/mu';The Head Curve of the Pump'H=A-B*Q^2';The Volumetric Flowrate'Q=Pi*Dia^2/4*V';The Friction Factorf= 'piecewise(Ren>2300,(1/sqrt(f)=-2*log10((e/Dia)/'3.7' + 2.51/(Ren*sqrt(f)))), Ren<=2300,64/Ren)';
<Text-field style="Heading 1" layout="Heading 1">Physical Parameters and Results</Text-field>
Physical ParametersWater Viscosity\316\274Pa sWater Density\317\201kg 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 of PipeDiamLength of PipeLmPipe roughnessemPump Head Curve 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
Resultsrestart;
use DocumentTools in
g:=9.81:
e:=parse(GetProperty(TextArea4, value)):
mu:=parse(GetProperty(TextArea0,value)):
rho:=parse(GetProperty(TextArea1,value)):
Dia:=parse(GetProperty(TextArea2,value)):
L:=parse(GetProperty(TextArea3,value)):
A:=parse(GetProperty(TextArea5,value)):
B:= parse(GetProperty(TextArea6,value)):
Bernoulli:='g*H(Q(V))='fric(Ren(V))'*L/Dia*V^2/2':
Ren:=V->Dia*V*rho/mu:
H:=Q->A-B*Q^2:
Q:=V->Pi*Dia^2/4*V:
fric:=(Ren)-> piecewise( Ren>2300,fsolve (1/sqrt(f)=-2*log10((e/Dia)/3.7 + 2.51/(Ren*sqrt(f))),f), Ren<=2300,64/Ren):
V_ans:=fsolve( Bernoulli,V=1):
SetProperty(Label0,caption,sprintf("%0.3g",V_ans)):
SetProperty(Label1,caption,sprintf("%0.3g",evalf(Q(V_ans)))):
SetProperty(Label2,caption,sprintf("%0.3f",evalf(Ren(V_ans)))):
SetProperty(Label3,caption,sprintf("%0.3g",evalf(H(Q(V_ans))))):
end use;
Liquid Velocity in Exit 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Reynolds NumberReHead Produced by PumpH(Q)m
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