May-01-2018, 02:59 PM
This is an exercise i'm working with, and I'm wondering if anyone have the chance to help me with this.
Problem description:
Water towers are among the simplest yet ingenious methods to distribute water having been in use in some form since ancient times. More than simply calculating capacity or flow rate however, we can model how a tank can be filled and emptied. We will model a scaled down version of this problem. In our model, our water tank will have a single water flow inward, and a single flow outward and be perfectly cylindrical.
where:
fin – the flow-rate in (cubic meters per second)
fout – the flow rate out ( cubic meters per second )
r – the radius of the tower (meters)
H – The height of the tower (meters)
h – The height of the current water-level (meters)
You are tasked to write a function called ‘trackFlow’ which when given some initial conditions iteratively simulates the contents of the tower. By ‘iteratively’ we mean you will update the volume of water in the tank repeatedly over numerous time-intervals.
More specifically, the tank will be filled up until some time (topen) at which point the outward flow is activated (instantly).
Your function will accept the following arguments (in the following order):
fin – The flow-rate in ( cubic meters per second )
fout – The flow rate out ( cubic meters per second )
r – The radius of the tower (meters)
H – The height of the tower (meters)
h – The height of the initial water-level (meters)
tmax – The maximum time allowed to simulate the system(seconds)
topen – The time when the outwards flow opens (seconds)
Your calculations should continue until either t > tmax, h > H or h < 0 whichever comes first.
Assume
The time-step = 0.1 sec
The density of water = 1000 Kg/m3
The inward flow is open at t = 0.0 sec
Your function should return the following
A list of volume values (in cubic meters )
A list of water-height values (in meters)
A list of time-stamps at which the values were calculated (in seconds)
Note: Do not print the lists in a formatted manner, simply return them at the end of calculations
All values during the computation must be rounded to 10 decimal places to avoid approximation problem. See details at
https://docs.python.org/2/tutorial/floatingpoint.html
In addition, all output values are to be rounded to 2 decimal places when they are appended to the output result-arrays.
See the round() function for more information.
Your submission will be tested against a sample solution with numerous test-cases in addition to those presented below.
Sample testing data:
testFlow(1, 1, 1, 10, 0, 3, 1) #Steady-state after 1s
Volumes = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
Heights = [0, 0.03, 0.06, 0.1, 0.13, 0.16, 0.19, 0.22, 0.25, 0.29, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32]
Times = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0]
testFlow(1, 5, 1, 10, 0, 5, 2) #Decreases until tank is empty
Volumes = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 1.6, 1.2, 0.8, 0.4]
Heights = [0, 0.03, 0.06, 0.1, 0.13, 0.16, 0.19, 0.22, 0.25, 0.29, 0.32, 0.35, 0.38, 0.41, 0.45, 0.48, 0.51, 0.54, 0.57, 0.6, 0.64, 0.51, 0.38, 0.25, 0.13]
Times = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4]
testFlow(1, 0.5, 1, 10, 0, 3, 1) #Increases after out-flow is open to maximum time
Volumes = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.05, 1.1, 1.15, 1.2, 1.25, 1.3, 1.35, 1.4, 1.45, 1.5, 1.55, 1.6, 1.65, 1.7, 1.75, 1.8, 1.85, 1.9, 1.95, 2.0]
Heights = 0, 0.03, 0.06, 0.1, 0.13, 0.16, 0.19, 0.22, 0.25, 0.29, 0.32, 0.33, 0.35, 0.37, 0.38, 0.4, 0.41, 0.43, 0.45, 0.46, 0.48, 0.49, 0.51, 0.53, 0.54, 0.56, 0.57, 0.59, 0.6, 0.62, 0.64]
Times = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0]
My code is:
import math
"""f_in = int()
f_out = int()
r = int()
H = int()
h = int()
t_max = int()
t_open = int()"""
def trackFlow(f_in, f_out, r, H, h, t_max, t_open): #Function with input values
t = 0
pi = math.pi
Volume = [] #Making list for volumes
Heights = [] #Making list for heights
Times = [] #Making list for times
t = 0
v_old = pi*r**2*h #Defining the start volume of water.
v_total = pi*r**2*H #Defining the total volume in the tank
Heights.append(h)
Volume.append(v_old)
Times.append(0)
while t < t_open: #Make a loop for filling up the tank
v_new = v_old + (f_in*(0.1)) #An equation for the volume of water after time, t.
t+=0.1 #Get the loop for checking for t0, t1+0.1, t2+0.1
v_old = v_new #v_new becomes v_old when the loop checks for next t.
h_new = h + ((f_in*(t))/(pi*r**2)) #The height after time, t, before tank is filled
Heights.append(round(h_new,2)) #Adding heights before tank is filled
Times.append(round(t,2)) #Adding time-stamps
Volume.append(round(v_new,2)) #Adding the volume in the list Volume
if t > t_open: #Make an if statement to break the loop if the
break #water volume gets bigger than tank volume.
elif h > H:
break
elif h < 0:
break
else:
continue
while t_open < t < t_max: #Making a loop for when the outward flow has started.
v_new = v_old + ((f_in - f_out)*(t_max-t)) #Equation for water volume after time t, f_out has been taken into consideration.
t = t_open #t counts from t_open
t+=0.1 #And checking for each value in the interval 0.1
h_new = h + (((f_in - f_out)*(t_max-t))/(pi*r**2)) #Equation for water height after time t, f_out has been taken into consideration.
Volume.append(round(v_new,2)) #Adding heights after the outward flow has started
Heights.append(round(h_new,2)) #Adding heights after the outward flow has started
Times.append(round(t,2)) #Adding time-stamps, still supposed to still add 0.1
if t > t_max: #Make an if statement to break the loop if the
break
elif h > H:
break
elif h < 0:
break
else:
continue
"""Volume = (round(Volume,2))
Heights = (round(Heights,2))
Times = (round(Times,2))"""
print(Volume) #Print list with volumes
print(Heights) #Print list with heights
print(Times) #Print list with time-stamps
I think my problem is I don't get the second loop to work and I need some help.
I appreciate all assistance and guidance You may support me with.
Problem description:
Water towers are among the simplest yet ingenious methods to distribute water having been in use in some form since ancient times. More than simply calculating capacity or flow rate however, we can model how a tank can be filled and emptied. We will model a scaled down version of this problem. In our model, our water tank will have a single water flow inward, and a single flow outward and be perfectly cylindrical.
where:
fin – the flow-rate in (cubic meters per second)
fout – the flow rate out ( cubic meters per second )
r – the radius of the tower (meters)
H – The height of the tower (meters)
h – The height of the current water-level (meters)
You are tasked to write a function called ‘trackFlow’ which when given some initial conditions iteratively simulates the contents of the tower. By ‘iteratively’ we mean you will update the volume of water in the tank repeatedly over numerous time-intervals.
More specifically, the tank will be filled up until some time (topen) at which point the outward flow is activated (instantly).
Your function will accept the following arguments (in the following order):
fin – The flow-rate in ( cubic meters per second )
fout – The flow rate out ( cubic meters per second )
r – The radius of the tower (meters)
H – The height of the tower (meters)
h – The height of the initial water-level (meters)
tmax – The maximum time allowed to simulate the system(seconds)
topen – The time when the outwards flow opens (seconds)
Your calculations should continue until either t > tmax, h > H or h < 0 whichever comes first.
Assume
The time-step = 0.1 sec
The density of water = 1000 Kg/m3
The inward flow is open at t = 0.0 sec
Your function should return the following
A list of volume values (in cubic meters )
A list of water-height values (in meters)
A list of time-stamps at which the values were calculated (in seconds)
Note: Do not print the lists in a formatted manner, simply return them at the end of calculations
All values during the computation must be rounded to 10 decimal places to avoid approximation problem. See details at
https://docs.python.org/2/tutorial/floatingpoint.html
In addition, all output values are to be rounded to 2 decimal places when they are appended to the output result-arrays.
See the round() function for more information.
Your submission will be tested against a sample solution with numerous test-cases in addition to those presented below.
Sample testing data:
testFlow(1, 1, 1, 10, 0, 3, 1) #Steady-state after 1s
Volumes = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
Heights = [0, 0.03, 0.06, 0.1, 0.13, 0.16, 0.19, 0.22, 0.25, 0.29, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32, 0.32]
Times = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0]
testFlow(1, 5, 1, 10, 0, 5, 2) #Decreases until tank is empty
Volumes = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 1.6, 1.2, 0.8, 0.4]
Heights = [0, 0.03, 0.06, 0.1, 0.13, 0.16, 0.19, 0.22, 0.25, 0.29, 0.32, 0.35, 0.38, 0.41, 0.45, 0.48, 0.51, 0.54, 0.57, 0.6, 0.64, 0.51, 0.38, 0.25, 0.13]
Times = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4]
testFlow(1, 0.5, 1, 10, 0, 3, 1) #Increases after out-flow is open to maximum time
Volumes = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.05, 1.1, 1.15, 1.2, 1.25, 1.3, 1.35, 1.4, 1.45, 1.5, 1.55, 1.6, 1.65, 1.7, 1.75, 1.8, 1.85, 1.9, 1.95, 2.0]
Heights = 0, 0.03, 0.06, 0.1, 0.13, 0.16, 0.19, 0.22, 0.25, 0.29, 0.32, 0.33, 0.35, 0.37, 0.38, 0.4, 0.41, 0.43, 0.45, 0.46, 0.48, 0.49, 0.51, 0.53, 0.54, 0.56, 0.57, 0.59, 0.6, 0.62, 0.64]
Times = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0]
My code is:
import math
"""f_in = int()
f_out = int()
r = int()
H = int()
h = int()
t_max = int()
t_open = int()"""
def trackFlow(f_in, f_out, r, H, h, t_max, t_open): #Function with input values
t = 0
pi = math.pi
Volume = [] #Making list for volumes
Heights = [] #Making list for heights
Times = [] #Making list for times
t = 0
v_old = pi*r**2*h #Defining the start volume of water.
v_total = pi*r**2*H #Defining the total volume in the tank
Heights.append(h)
Volume.append(v_old)
Times.append(0)
while t < t_open: #Make a loop for filling up the tank
v_new = v_old + (f_in*(0.1)) #An equation for the volume of water after time, t.
t+=0.1 #Get the loop for checking for t0, t1+0.1, t2+0.1
v_old = v_new #v_new becomes v_old when the loop checks for next t.
h_new = h + ((f_in*(t))/(pi*r**2)) #The height after time, t, before tank is filled
Heights.append(round(h_new,2)) #Adding heights before tank is filled
Times.append(round(t,2)) #Adding time-stamps
Volume.append(round(v_new,2)) #Adding the volume in the list Volume
if t > t_open: #Make an if statement to break the loop if the
break #water volume gets bigger than tank volume.
elif h > H:
break
elif h < 0:
break
else:
continue
while t_open < t < t_max: #Making a loop for when the outward flow has started.
v_new = v_old + ((f_in - f_out)*(t_max-t)) #Equation for water volume after time t, f_out has been taken into consideration.
t = t_open #t counts from t_open
t+=0.1 #And checking for each value in the interval 0.1
h_new = h + (((f_in - f_out)*(t_max-t))/(pi*r**2)) #Equation for water height after time t, f_out has been taken into consideration.
Volume.append(round(v_new,2)) #Adding heights after the outward flow has started
Heights.append(round(h_new,2)) #Adding heights after the outward flow has started
Times.append(round(t,2)) #Adding time-stamps, still supposed to still add 0.1
if t > t_max: #Make an if statement to break the loop if the
break
elif h > H:
break
elif h < 0:
break
else:
continue
"""Volume = (round(Volume,2))
Heights = (round(Heights,2))
Times = (round(Times,2))"""
print(Volume) #Print list with volumes
print(Heights) #Print list with heights
print(Times) #Print list with time-stamps
I think my problem is I don't get the second loop to work and I need some help.
I appreciate all assistance and guidance You may support me with.