You are designing a centrifugal compressor system to compress hydrogen at 200 kP

Question

You are designing a centrifugal compressor system to compress hydrogen at 200 kPa (absolute) to 7,000 kPa (absolute) discharge pressure in order to inject the gas into a transmission line. The steady-state inlet and outlet temperatures are 290 degrees K and 460 degrees K, respectively. The poetential and kenetic energy changes through the compressor are essentially zero (0). The metered mass flow rate of hydrogen in 5.0 kg/s, and 20 kJ/kg heat loss to the atmosphere is estimated. Assuming hydrogen to be an ideal gas, determine the required power input to operate this compressor.

Please show work so I'll understand how the answer was found. Thanks!

Explanation / Answer

mass flow rate = 5 kg/s = 5000/2 mol/s = 2500 mol/s

now, applying energy conservation,

power input to compressor = change in internal energy of H2 + loss to atmosphere

here, change in internal energy of H2 = outlet energy - inlet energy ......for the gas energy can be measured in terms of PV work, hence

change in internal energy of H2 = P1*V1 - P2*V2 = n*R*T2 - n*R*T1 = n*R*(T2-T1),

where n= no of moles of H2 = 2500 mol/s (calculated above), R= 8.314 J/mol-K

therefore change in internal energy of H2 = 2500*8.314*(460-290) = 3533450 J/s = 3533.45 KJ/s

and loss to atmosphere = flow rate * 20 KJ/Kg = 5Kg/s * 20 KJ/kg = 100 KJ/s

substituting these values in the above energy conservation equation, we get...

power input to compressor = 3533.45 KJ/s + 100 KJ/s = 3633.45 KJ/s

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.