luid and Preumatica Conrol ETS2300C Spring 2018 Wate, is to wing ara votamete lo

Question

luid and Preumatica Conrol ETS2300C Spring 2018 Wate, is to wing ara votamete low rate :10 gallonssec trough Ihree sechons of a honzuntai pipe lie. hi sha) wth cross-sectional areas of Ar 5 Usng the information provided below the foure a. What is the fow velocty U: in fUsec in Secion 1? b. Whart is the fow velocity Us in tusec in Section 3 t What is the peessure Ps in psig irP-10 pag? d. What is the differentail pressure (AP) bebenen Secton 1 and Section 32 1- TUS Galon “ 231 i? g gravitational constant-322 rtsec Conservation of Mass EquationpAU-constant Benoulis& Equation Page 4 of 6

Explanation / Answer

given:

Q=10 gallons/sec=10*231 in^3/sec=2310 in^3/sec

A1=5 in^2

A2=3 in^2

A3=7 in^2

density=pho=62.32 lb/ft^3=0.036065 lb/in^3

g=32.2 ft/sec^2=386.4 in/sec^2

part a:

flow velocity U1=Q/(A1)=462 in/sec=38.5 ft/s

part b:

flow velocity U3=Q/A3=330 in/s=27.5 ft/s

part c:

using bernoulli’s equation:

P+(0.5*pho*v^2/g)=constant

writing bernoulli’s equation between section 1 and section 3:

P1+(0.5*pho*U1^2/g)=P3+(0.5*pho*U3^2/g)

==>10+(0.5*0.036065*462^2/386.4)=P3+(0.5*0.036065*330^2/386.4)

==>P3=10+(0.5*0.036065*462^2/386.4)-(0.5*0.036065*330^2/386.4)=14.879 psig

part d:

differential pressure=P3-P1=4.879 psig

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