%3Cp%3E1.%20What%20three%20quantities%20are%20always%20conserved%3F%3C%2Fp%3E%0A
ID: 3895240 • Letter: #
Question
%3Cp%3E1.%20What%20three%20quantities%20are%20always%20conserved%3F%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E2.%20In%20steady%20state%20flow%20of%20a%20fluid%20what%20physical%20quantity%20is%0Aalways%20conserved%3F%20If%20the%20density%20of%20the%20fluid%20is%20a%20constant%20what%0Aadditional%20physical%20quantity%20is%20conserved%3F%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E3.%20Write%20darcy's%20law%20for%3A%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Ea.%20incompressible%20flow%20through%20a%20cylinder%20of%20length%20L%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Eb.%20compressible%20(ideal%20gas)%20flow%20through%20a%20cylinder%20of%20length%0AL%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E4.%20Consider%20the%20following%20structure%3A%20An%208%20inch%20diameter%20casing%0A(impermeable%20metal%20pipe)%20extends%207000%20feet%20into%20the%20ground.%20The%0Acasing%20is%20empty%20and%20clear%20of%20obstruction%20except%20for%20the%20last%202%20feet%0Awhich%20contains%20a%20permeable%20plug%20(k%3D100%20mD).%20Outside%20the%20plug%20(point%0AA)%20is%20an%20essentially%20inexhaustible%20source%20of%20ideal%20gas%20at%20200%0Aatmospheres%20pressure%20and%20125%20degrees%20celsius.%20The%20top%20of%20the%20casing%0Ahas%20a%20regulator%20that%20feeds%20the%20gas%20into%20a%20processing%20pipe%20line%20at%205%0Aatmospheres%20and%2025%20degrees%20celsius.%20The%20flow%20rate%20of%20this%200.02%20cp%0Aideal%20gas%20into%20the%205%20atmosphere%20pipe%20line%20(point%20C)%20is%2010000%0Acm%5E3%2Fsec.%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3EP_A%3D200%20atm%3C%2Fp%3E%0A%3Cp%3ET_A%3D125%20degrees%20celsius%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3EP_B%3D10%20atm%3C%2Fp%3E%0A%3Cp%3ET_B%3D115%20degrees%20celsius%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3EP_C%3D5%20atm%3C%2Fp%3E%0A%3Cp%3ET_C%3D25%20degrees%20celsius%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Ea.%20Remembering%20that%201%20inch%3D2.54%20cm%2C%20what%20is%20the%20volume%20flow%20rate%0Ainto%20the%20pug%20at%20point%20A%3F%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Eb.%20What%20is%20the%20volume%20flow%20rate%20leaving%20the%20plug%20at%20point%20B%3F%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E5.%20Consider%20the%20following%20pipe%20assembly%20containing%20two%20permeable%0Afilters%20each%20of%20length%20L%20seperated%20by%20an%20equal%20distance.%20The%20cross%0Asectional%20areas%20are%20A%2C%20and%20the%20filters%20have%20permeabilities%20k1%20and%0Ak2.%20An%20incompressible%20fluid%20of%20viscosity%20u%20flows%20through%20this%0Asystem%20at%20a%20volume%20flow%20rate%20of%20Q.%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3EThe%20input%20pressure%20P_i%2C%20the%20output%20pressure%20is%20P_o%20and%20the%0Apressure%20between%20the%20is%20P_m.%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Ea.%20Derive%20an%20expression%20relating%20k1%2C%20k2%2C%20and%20the%20three%20pressures%0AP_i%2C%20P_o%2C%20and%20P_m.%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Eb.%20If%20P_i%20%3D%2010%20atmospheres%2C%20P_m%20%3D%203%20atmospheres%20%2C%20P_o%20%3D%201%0Aatmosphere%20and%20k2%20%3D%20700%20mD%20what%20is%20the%20value%20of%20k1%3F%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3Ec.%20If%20in%20addition%20you%20are%20told%20the%20fluid%20viscosity%20is%207%20cp%2C%20the%0Alength%20L%3D20%20cm%20and%20the%20area%20A%20is%2040cm%5E2%20what%20is%20the%20volume%20flow%0Arate%3F%3C%2Fp%3E%0AExplanation / Answer
kinetic energy and momentum are conserved
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