(QUESTION) Using the required programming language (python, matlab, etc.) plot the variation of pressure on the piston surface as a function of time until the piston moves 9 m, with the help of the following commands below. This problem will be solved for U_p =1, 4, 16, 64, 256 m/s. We'll assume that the time starts at t = 0 when the piston starts moving. (PLEASE TAKE A SCREENSHOT OF THE PLOTTING AND OTHER RESULTS.) Note: Since we don't have the exact time intervals or the rate at which the piston moves, we'll assume a constant speed and divide the distance by the speed to get the time taken. (QUESTION) COMMANDS import matplotlib.pyplot as plt import numpy as np # Given parameters diameter = 0.1 # meters length = 10 # meters initial_pressure = 10e3 # Pascals initial_temperature = 288 # Kelvin # Convert diameter to radius radius = diameter / 2 # Calculate initial and final volumes initial_volume = np.pi * radius**2 * length final_volume = np.pi * radius**2 * (length - 9) # Calculate initial and final pressures initial_pressure = initial_pressure final_pressure = (initial_pressure * initial_volume) / final_volume # Time taken for piston to move 9 m (distance / speed) time_taken = 9 / np.array([1, 4, 16, 64, 256]) # Calculate pressures at each time step pressures = final_pressure * np.ones_like(time_taken) # Plotting plt.plot(time_taken, pressures, 'o-') plt.xlabel('Time (s)') plt.ylabel('Pressure on Piston Surface (Pa)') plt.title Conclusion: Using the codes above, we need to calculate the pressure on the piston surface at different time steps for different piston speeds (U_p):
(QUESTION) Using the required programming language (python, matlab, etc.) plot the variation of pressure on the piston surface as a function of time until the piston moves 9 m, with the help of the following commands below. This problem will be solved for U_p =1, 4, 16, 64, 256 m/s. We'll assume that the time starts at t = 0 when the piston starts moving. (PLEASE TAKE A SCREENSHOT OF THE PLOTTING AND OTHER RESULTS.)
Note: Since we don't have the exact time intervals or the rate at which the piston moves, we'll assume a constant speed and divide the distance by the speed to get the time taken.
(QUESTION) COMMANDS
import matplotlib.pyplot as plt
import numpy as np
# Given parameters
diameter = 0.1 # meters
length = 10 # meters
initial_pressure = 10e3 # Pascals
initial_temperature = 288 # Kelvin
# Convert diameter to radius
radius = diameter / 2
# Calculate initial and final volumes
initial_volume = np.pi * radius**2 * length
final_volume = np.pi * radius**2 * (length - 9)
# Calculate initial and final pressures
initial_pressure = initial_pressure
final_pressure = (initial_pressure * initial_volume) / final_volume
# Time taken for piston to move 9 m (distance / speed)
time_taken = 9 / np.array([1, 4, 16, 64, 256])
# Calculate pressures at each time step
pressures = final_pressure * np.ones_like(time_taken)
# Plotting
plt.plot(time_taken, pressures, 'o-')
plt.xlabel('Time (s)')
plt.ylabel('Pressure on Piston Surface (Pa)')
plt.title
Conclusion: Using the codes above, we need to calculate the pressure on the piston surface at different time steps for different piston speeds (U_p):
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