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How to Determine the Loop Pressure Sample Size

Though few are aware of the meaning of loop pressure, it's a concept that has wide-ranging practical applications. Loop pressure is a thermodynamic concept that measures the volume-pressure relationship in a given system, from the starting point to the completion of the loop, or cycle. In large systems, it's more efficient to take a sample size in order to extrapolate the measurement to the whole. You can calculate the sample size of loop pressure according to the formula μ = AC^2 + C + C(e)V^2. The symbol "^" denotes something raised to a power; in other words, "V squared" or "C squared." In mathematical notation, adjacent terms are assumed to be multiplied; for example, C(e) means "C times e."

Instructions

- 1
  Determine C, which is the pressure at a given point in the system; for example, 10 pounds per square inch.
- 2
  Input for the total volume, V, of the system and square it. For example, if the volume of the system is 50 cubic inches, you would multiply 50 by 50 to get 2,500 cubic inches.
- 3
  Calculate A, the loop ratio, which is determined by dividing the loop total distance by sample distance. If the total distance of the hypothetical system is 10 feet, divide that by an arbitrary sample distance of 2 feet, which is 5 feet. You can pick any sample distance, as long as you use it consistently in your calculation of the loop-pressure sample size.
- 4
  Input for e, which is the duration (time) it takes for the loop to complete one cycle; for example, e=60 seconds.
- 5
  Calculate the values to solve for μ, which is the sample size. Using the figures from the example, it would be 5(100) + 10 + (10)(60)(2,500), or 1,500,510 units.

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