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Dear!

I have a problem with one, complex exercise. I’ve divided it into three parts just to simplify finding the answer. So let’s start.

The air is sucked from the atmosphere by a compressor. Atmospheric pressure is 0,1MPa and the temperature is 283K, the suction pressure in the compressor is 1.5 MPa, whereas the discharge 4,5MPa and its temperature is 323K. Capacity of the compressor is 60000m3 /h. I need to analyse the important aspects related to the profitability of the operation of the installation (?) and first of all the energy balance. I do not know whether they are here given all the information necessary to solve the problem, but in case of any doubts my job is to ask for a specific data.

I divided this task into three parts,:

1. Compression of air (isentropic? I suppose).

2. Air Transport pipeline (adiabatically, with friction)

3. The expansion ((isentropic? I suppose).

1. Compression of air

In order to determine the technical work required to compress the air used the dependence of transformation polytropy:

Lt = (1 / (m-1)) * (p1V1-p2V2) + p1V1-p2V2

Just do not know how do I get m. Any suggestions?

2

I skip the phenomena which are taking place in the pipeline e.x pressure loss due to friction and due to local resistance. I assume that the temperature of the air in the pipe at the inlet = temperature of the air in the pipe at the outlet and the inlet pressure equal to the pressure of the outlet.

3. The expansion

The temperature in the nozzle outlet cross-section is:

T2 = T1-ƞd (T1-T2S)

The temperature of the T2S the isentropic expansion may be determined by the formula

T1 / T2 = (V2 / V1) χ-1 = (p1 / p2) ^ ((χ-1) / χ), assuming the air getting χ = 1.4

T2S = 323 * 0.1 ^ (0.286) = 323 * 0.52 = 168K

thus

T2 = 323-0,90 * (323-168) = 183,5K

Is it the right solution? What else I need in order to develop the energy balance?

Dear!

I have a problem with one, complex exercise. I’ve divided it into three parts just to simplify finding the answer. So let’s start.

The air is sucked from the atmosphere by a compressor. Atmospheric pressure is 0,1MPa and the temperature is 283K, the suction pressure in the compressor is 1.5 MPa, whereas the discharge 4,5MPa and its temperature is 323K. Capacity of the compressor is 60000m3 /h. I need to analyse the important aspects related to the profitability of the operation of the installation (?) and first of all the energy balance. I do not know whether they are here given all the information necessary to solve the problem, but in case of any doubts my job is to ask for a specific data.

I divided this task into three parts,:

1. Compression of air (isentropic? I suppose).

2. Air Transport pipeline (adiabatically, with friction)

3. The expansion ((isentropic? I suppose).

1. Compression of air

In order to determine the technical work required to compress the air used the dependence of transformation polytropy:

Lt = (1 / (m-1)) * (p1V1-p2V2) + p1V1-p2V2

Just do not know how do I get m. Any suggestions?

2

I skip the phenomena which are taking place in the pipeline e.x pressure loss due to friction and due to local resistance. I assume that the temperature of the air in the pipe at the inlet = temperature of the air in the pipe at the outlet and the inlet pressure equal to the pressure of the outlet.

3. The expansion

The temperature in the nozzle outlet cross-section is:

T2 = T1-ƞd (T1-T2S)

The temperature of the T2S the isentropic expansion may be determined by the formula

T1 / T2 = (V2 / V1) χ-1 = (p1 / p2) ^ ((χ-1) / χ), assuming the air getting χ = 1.4

T2S = 323 * 0.1 ^ (0.286) = 323 * 0.52 = 168K

thus

T2 = 323-0,90 * (323-168) = 183,5K

Is it the right solution? What else I need in order to develop the energy balance?

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