Air enters a compressor at ambient conditions of 15 psia and 60^∘ F with a low velocity and exit

step 1 So here we have air that's going into a compressor. Let's see here. At ambient conditions, so 15

Air enters a compressor at ambient conditions of 15 psia and...

Air enters a compressor at ambient conditions of 15 psia and $60^{\circ} \mathrm{F}$ with a low velocity and exits at 150 psia, $620^{\circ} \mathrm{F}$, and $350 \mathrm{ft} / \mathrm{s}$. The compressor is cooled by the ambient air at $60^{\circ} \mathrm{F}$ at a rate of $1500 \mathrm{Btu} / \mathrm{min}$. The power input to the compressor is 400 hp. Determine $(a)$ the mass flow rate of air and $(b)$ the portion of the power input that is used just to overcome the irreversibilities.

Key Concepts

Irreversibility and Exergy Destruction

In real devices, processes are not perfectly efficient because of inherent losses due to friction, heat transfer to surroundings, and other non-idealities. This concept involves quantifying the portion of the input power that is 'lost' through these irreversibilities, which can be analyzed using exergy (or availability) analysis to understand how much energy is actually useful.

Compressor Performance and Work Analysis

This concept pertains to understanding how compressors add energy to a fluid by doing work on it, resulting in a rise in pressure, temperature, and sometimes velocity. By connecting the power input to the fluid’s enthalpy change (via mass flow rate), one can gauge the compressor’s performance and determine the effective energy transfer to the fluid.

Open System Energy Balance

This concept involves applying the First Law of Thermodynamics to a control volume, where mass and energy cross the system boundary. It is used to relate power input, heat transfer, and changes in fluid properties (like enthalpy) to determine unknown quantities, such as the mass flow rate in the compressor.

Steady?Flow Energy Equation

Focusing on systems where properties remain constant over time, the steady-flow energy equation expresses that the net rate of energy added (in the form of heat and work) equals the change in enthalpy and kinetic or potential energy of the fluid. This equation is central to analyzing and solving problems with compressors or turbines.

Transcript

00:01 So here we have air that's going into a compressor.

00:06 Let's see here.

00:08 At ambient conditions, so 15 psi absolute and 65 degrees f.

00:14 It's going in at a negligible velocity, so we'll say that v1 is roughly zero.

00:20 It's coming out of the compressor at 150 psia and 620 degrees fahrenheit.

00:32 And also with a speed of 350 feet per second.

00:39 Now, we're told also that, let's see here, we have the compressors cooled from the ambient conditions with at a rate of 1500 btu per minute.

00:51 So again, we need to be careful and make sure that we give some unit convergence on this.

00:58 And we're also told that the compressor, the power import to the compressor is 400 horsepower.

01:04 Again, we're going to have to do some unit conversion on there to btu per second.

01:11 Now, we have, what do we have here? so we want to figure out the mass flow rate and the proportion of the power input that is used just to overcome the irreversibilities.

01:25 Well, the mass flow rate of the air, we can figure out the, well, we have the ideal gas constant for the air.

01:38 So we can figure out the enthalpy at the inlet and the standard entropy at the inlet and likewise at the exit, the enthalpy and the standard entropy.

01:46 And so we know it's steady states.

01:47 So the work coming in is the energy flow in equals the energy flow out.

01:52 So that means w .n plus m.

01:54 Times h1 plus v1 squared over 2 must be equal to m...

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