Reciprocating machine power calculation
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The technical manual for piston compressors provides two formulas for calculating the power required for actual gases. Formula 1 is: P=1.634×Ps×Vt……, and Formula 2 is: P=n÷60×Ps×Vt…… (the expressions after the ellipsis are the same, so they aren’t written in full here). The values obtained using these two formulas differ significantly depending on the rotational speed. So, where does 1.634 come from? Why are these two formulas different and yet appear in a handbook edited by the same person?
The question is quite profound; I took a look and noticed that the units in these two formulas are different. 1. In the first formula, the unit of P is Kg/cm^2, with 1 Kg/cm^2 equal to 9.8x10^4 N/m^2; the unit of Vt is m^3/min, and 1 m^3/min equals 1/60 m^3/s. Next, divide all the values of w (or joules) by 1000 to convert them into Kw. This gives us 9.8×10000/1000/60 = 1.6333. In the second formula, the unit of P is MPa, with 1 MPa equal to 1,000,000 Pa; the unit of Vt is m^3/r (the working volume per revolution), and by multiplying this by the number of revolutions per second of the motor, namely n/60, we get m^3/s (the volume per second). Again, divide all the values of w (or joules) by 1000 to convert them into Kw. The result obtained using this formula is 1,000,000×n/60/1000. This formula should also be multiplied by 1000 to get the result in Kw.
The second formula is incorrect; 1000 is missing in the multiplication
First of all, thank you for your answer. The first formula was easy to understand right after I posted this, but I took a closer look at the second formula: Ps should not be in MPa units, it has to be in Pa units for the formula to be correct; therefore, there’s no need to multiply by 1000.
The formula is correct; the pressure unit should be Pa