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Chapter 2

Chapter 2#

Question #14: Pressurized Air#

A piston with \(m=2\:kg\) mass is used to store air in a piston-and-cylinder system with a diamater of \(D=10\:cm\). Assuming the pressure of the atmosphere around this system is \(P_{atm}=101\:kPa\), calculate the pressure of air stored inside this system.

CH2-Q14.jpg

From pressure definition

\(P=F/A\)

and

\(A=\pi D^2/4\)

the gravitational force by the piston

\(F=mg\)

The pressure of air inside is composed of the pressure at the atmosphere around in addition to the pressure inposed by the cylinder weights

\(P_{air}=P+P_{atm}\)

#import libraries
import numpy as np

#define variables
P_atm = 101E+3   #pressure around the system in Pa
m = 2   #piston weight in kg
D = 0.1   #piston diameter in m
g = 9.81   #gravitational acceleration in m/s2

F = m * g   #gravitaional force by the piston
A = np.pi * D ** 2 / 4   #piston surface area in m2

P = F / A   #pressure imposed by the piston weight

P_air = P_atm + P   #total pressure of air stored


print('The pressure of air stored in the system is', f"{P_air/1000:.1f}", 'kPa')

The pressure of air stored in the system is 103.5 kPa
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