Physics, asked by ravikant12233, 1 month ago

Determine the size of the cylinder for a double acting air compressor of 40kw indicated Power in which air is drawn in at 1 bar &15°c and compressed according to the law PV^1.2= constant to 6 bar. The compressor runs at 100 rpm with average piston speed of 152.5 m/min. Neglect clearance.​

Answers

Answered by maitreepanda129
0

Answer:

Determine the size of the cylinder for a double acting air compressor of 40kw indicated Power in which air is drawn in at 1 bar &15°c and compressed according to the law PV^1.2= constant to 6 bar. The compressor runs at 100 rpm with average piston speed of 152.5 m/min. Neglect clearance.

Answered by anjali13lm
0

Answer:

The size of the cylinder for a double-acting compressor is 0.42m.

Explanation:

Given,

The power of a compressor, P = 40kW

The average speed of piston = 152.5m/min = 2.54m/s

The speed of the compressor, N = 160rpm = 2.66rps

Pressure, P₁ = 1bar = 100 kN/m^{2}

Pressure, P₂ = 6bar = 600 kN/m^{2}

PV^{1.2} = Constant,  

Therefore, n = 1.2

Hence, it is a polytropic process, in which heat and work done goes in the same direction.

Size of the cylinder, d =?

 As we know,

  • The average piston speed = 2lN

Here,

  • l = length
  • N = speed of the compressor

Therefore,

  • The average piston speed = 2lN = 2.54 m/s
  • 2\times l\times 2.66 = 2.54
  • l = 0.47 m

Now, we have to find out the volume by using the equation given below:

  • V = \frac{\pi }{4} d^{2} l

Here, d = size of the cylinder.

  • V = \frac{3.14 }{4} d^{2}\times 0.47
  • V = 0.368 d^{2}

As we know,

  • Power can be calculated by the equation given below:
  • P = 2\times W \times N    -------equation (1)

Here,

  • P = power
  • W = work done
  • N = speed of the compressor

For this, we have to calculate the work done for the polyprotic process

  • W = \frac{n}{n -1 } (P_{1}V_{1}  )[\frac{P_{2} }{P_{1} }^{\frac{n-1}{n} } - 1]

After putting the given values in the equation, we get:

  • W = \frac{1.2}{1.2 -1 } (100\times 0.368d^{2}   )[\frac{600 }{100 }^{\frac{1.2-1}{1.2} } - 1]
  • W = 6\times 100\times 0.368d^{2} [ 6^{0.1} -1]
  • W = 6\times 100\times 0.368d^{2} [1.19 - 1]         ( 6^{0.1} = 1.19 )
  • W = 6\times 100\times 0.368d^{2} [0.19 ]
  • W = 41.9d^{2}

Now, after putting the value of work done in equation (1), we get:

  • P = 2\times 41.9d^{2}  \times 2.66
  • 40 = 2\times 41.9d^{2}  \times 2.66
  • d^{2} = 0.179
  • d = 0.42m

Hence, the size of the cylinder is 0.42m.

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