Chapter 2 Chapter 2 #

Question #14: Pressurized Air#

A piston with $m = 2 k g$ mass is used to store air in a piston-and-cylinder system with a diamater of $D = 10 c m$ . Assuming the pressure of the atmosphere around this system is $P_{a t m} = 101 k P a$ , calculate the pressure of air stored inside this system.

From pressure definition

$P = F / A$

and

$A = π D^{2} / 4$

the gravitational force by the piston

$F = m g$

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

$P_{a i r} = P + P_{a t m}$

#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

Chapter 2

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Chapter 2#

Question #14: Pressurized Air#

Chapter 2 #