our application is measure the tank Level using pressure sensor.then we convert the level to qty.
our problem is
temperature is decrease from 20 C to 4 C pressure level is also decrease(About 10 MM ).
we used following formula for Pressure to Level conversion
L = P / (ρ x g)
ρ = ρ0 x SG
ρ0 = Density of liquid (1000)
SG = 1.033 (at 4 C)
(we used density of milk = 1.003073 - 0.000179t - 0.000368F + 0.00374N)
where t = temperature in degrees C; F = percent fat; and N = percent nonfat
solids(SNF)
g = 9.80665 ms-2
Since you want for the application you want to design, that pressure do not change with the temperature changes, you can use the following sensors:
https://www.controleverything.com/content/Analog-Digital-Converters?sku=MS5637-02BA03_I2CS
https://www.controleverything.com/content/Pressure?sku=AMS5812_I2CS_0150-D-B
These sensors would require I2C interface with the controlling unit you are using.
If you will give me any idea about the controlling unit you are using I can further provide you with the codes and all.
I hope this helps you out.
Related
In Tinkercad, amplitude definition for Function Generators and scale definition for Oscilloscopes are quite confusing. Here is an ss from Tinkercad's function generator:
On the device 6.20 V is represented as peak-to-peak voltage, look at the red-lines I've marked. But on the panel right-hand-side, we input it as the amplitude, look at the green line I've marked. Which one is true?
And I cannot deduce the answer using an oscilloscope, because there is not enough info about oscilloscope. (At least, I couldn't find enough info.) Here is the input signal from the function generator above:
Answer is not obvious, because the meaning of 10 V placed on y_axis is ambiguous. Is it +/- 10 V as in 20 V in total, i.e. the voltage-per-division is 2 V (first explanation)? Or, is it +/- 5 V as in 10 V in total, i.e. voltage-per-division is 1 V (second explanation)? In some Youtube lectures the explanation is first one. But, I'm not quite sure. Because, if 6.2 V is amplitude and voltage-per-division is 2 V, then this is noncontradictory. But if 6.2 V is peak-to-peak voltage and voltage-per-division is 1 V, then this, too, is noncontradictory. Again, which one is true?
And also, while studying, I've realise that a real life experiment indicates that the second explanation should be true. Let me explain the experiment step by step.
Theory: Full Wave Rectifier Circuits
Assume we apply V_in as the amplitude, the peak-peak voltage is, V_peaktopeak = 2 * V_in. And for output signal we have,
V_out = (V_in - n * V_diode) * R_L / (R_L + r_d),
where n is the number of diode in conduction, V_diode is bias of a diode and R_L is load resistor. Load resistor is choosen big enough so that R_L >> r_d and we get,
V_out = V_in - n * V_diode.
In a real experiment r_d is in between 1 \ohm and 25 \ohm, and we choose R_L on the order of kilo \ohm. Therefore, we can ignore R_L / (R_L + r_d) part, safely.
And for DC voltage corresponding to the output signal we have,
V_DC = 2 * V_out / \pi = 0.637 * V_out.
Sheme of Circuit in an Experiment
Here is circuit scheme,
As you may see, for positive half-periode only two of four diode is in conduction. And for negative half-periode, the other two is in conduction. Thus n is 2 for this circuit. Let's construct this experiment on Tinkercad. I didn't use breadboard to show more similarity between the scheme of circuit and the circuit built in Tinkercad.
Scenerio #1 - Theoretical Expectations
Let's assume 6.2 V to be the amplitude. Then, V_in=6.2 V. And V_peaktopeak is 12.4 V. As output signal we calculate,
V_out = V_in - n * V_diode = 6.2 V - 2 * 0.7 V = 4.8 V.
And for DC equivalent we theoretically get,
V_DC = 0.637 * V_out = 3.06 V.
But in multimeter, we see 1.06 V. This indicates nearly %60 percantage error.
Scenerio #2 - Theoretical Expectations
Let's assume 6.2 V to be the peak-to-peak voltage. Then, V_in=3.1 V. And V_peaktopeak is 6.2 V. As output signal we calculate,
V_out = V_in - n * V_diode = 3.1 V - 2 * 0.7 V = 1.7 V.
And for DC equivalent we theoretically get,
V_DC = 0.637 * V_out = 1.08 V.
And in multimeter, we see 1.06 V. There values are pretty close to each other.
Conclusion
Based on these results, we may conclude that 6.2 V is peak-to-peak voltage, scheme on the function generator is true, the tag "Amplitude" in the description of function generator is wrong and the y-scale of an oscilloscope represents the total voltage half of which is positive and the other half is negative.
BUT
I cannot be sure, and since I'll teach this material in my electronic laboratory class, I really need to be sure about this conclusion. Therefore, here I'm asking you about your opinions, conclusions or maybe other references that I've missed.
TinkerCAD refers to peak-to-peak voltage as amplitude for some reason. I believe the second explanation (+/- 5V, 10 V total) is correct, based on the x axis and frequency value.
I am trying to solve a LP, which is a facility location problem.
The task asks me to deduct 10.000$ iff the optimal model results in having less than 3 Distribution Centers open (y1,y2,y3,y4).
The objective function looks like this: min z = Σ(fiyi) + ΣΣ(cijxij) + ΣΣ(xij*bi) - Σqi*10.000
fi: fixed costs
yi: binary variable; yi = 1 - DC is open; yi = 0 - DC is closed
cij: transportation costs from DC i to customer j
xij: quantity shipped from DC i to customer j
bi: variable warehouse costs at DC i
qi: binary variable; bi = 1 - IT Cost reduction yes; bi = 0 - no IT cost reduction
Now I need to introduce a logical constraint for having the "if..then..." thingy in it. I want to express the following dependence as a constraint in xpress:
if Σyi ≤ 2 ; then Σqi = 1 → IT cost reduction
if Σyi > 2 ; then Σqi = 0 → no IT cost reduction
Any help highly appreciated!
Solved it myself by introducing the following constraints:
3 ≤ Σyi + 2q ≤ 4
I am implementing a very simple animation effect for a game. The scenario is like this:
there is a elastic rubber line, length is 1 meter, when it is extended over 1 meter, it is elastic.
the line connects two dots A and B like this, the distance is S, S > 1 meter
A <------------- B
then fix dot A, and releases B, the line takes B to the direction of A
I want to know how to calculate time T, which B costs to move X meters towards A (X <= S).
Any ideas?
Thanks!
I have been meaning to learn how to animate these kinds of images in sage (a python based platform for math) for a while, so i used this as an excuse. I hope this code snippet and image is helpful.
A = 3
w = 0.5
# x = f(t) = A cos(wt) inside elastic region
# with x = displacement from 1 meter mark
# in the below code, x is the displacement from origin (x = A cos(wt) + 1)
# find speed when we cross the one meter mark
# f'(t) = -Aw sin(wt), but this is also max speed
# ie f'(t at one meter mark) = -Aw
speed_max = -A * w
# time to reach max speed + time to cross last meter
eta = float(pi/2 * 1/w + 1/abs(speed_max))
# the function you were looking for
def time_left(x):
if x < 1:
return x/abs(speed_max)
else:
return 1/w * arccos((x-1)/A)
It may not be clear in the image but within one meter of the origin there is no acceleration.
BFS(G,s)
1 for each vertex u ∈ G.V-{s}
2 u.color = WHITE
3 u.d = ∞
4 u.π = NIL
5 s.color = GRAY
6 s.d = 0
7 s.π = NIL
8 Q ≠ Ø
9 ENQUEUE(Q, s)
10 while Q ≠ Ø
11 u = DEQUEUE(Q)
12 for each v ∈ G.Adj[u]
13 if v.color == WHITE
14 v.color = GRAY
15 v.d = u.d + 1
16 v.π = u
17 ENQUEUE(Q, v)
18 u.color = BLACK
The above Breadth First Search code is represented using adjacency lists.
Notations -
G : Graph
s : source vertex
u.color : stores the color of each vertex u ∈ V
u.π : stores predecessor of u
u.d = stores distance from the source s to vertex u computed by the algorithm
Understanding of the code (help me if I'm wrong) -
1. As far as I could understand, the ENQUEUE(Q, s) and DEQUEUE(Q) operations take O(1) time.<br>
2. Since the enqueuing operation occurs for exactly one time for one vertex, it takes a total O(V) time.
3. Since the sum of lengths of all adjacency lists is |E|, total time spent on scanning adjacency lists is O(E).
4. Why is the running time of BFS is O(V+E)?.
Please do not refer me to some website, I've gone through many articles to understand but I'm finding it difficult to understand.
Can anyone please reply to this code by writing the time complexity of each of the 18 lines?
Lines 1-4: O(V) in total
Lines 5-9: O(1) or O(constant)
Line 11: O(V) for all operations of line 11 within the loop (each vertice can only be dequeued once)
Lines 12-13: O(E) in total as you will check through every possible edge once. O(2E) if the edges are bi-directional.
Lines 14-17: O(V) in total as out of the E edges you check, only V vertices will be white.
Line 18: O(V) in total
Summing the complexities gives you
O(4V + E + 1) which simplifies to O(V+E)
New:
It is not O(VE) because at each iteration of the loop starting at line 10, lines 12-13 will only loop through the edges the current node is linked to, not all the edges in the entire graph. Thus, looking from the point of view of the edges, they will only be looped at most twice in a bi-directional graph, once by each node it connects with.
I need to find the average Edit: total 2D velocity given multiple 2D velocities (speed and direction). A few examples:
Example 1
Velocity 1 is 90° at a speed of 10 pixels or units per second.
Velocity 2 is 270° at a speed of 5 pixels or units per second.
The average velocity is 90° at 5 pixels or units per second.
Example 2
Velocity 1 is 0° at a speed of 10 pixels or units per second
Velocity 2 is 180° at a speed of 10 pixels or units per second
Velocity 3 is 90° at a speed of 8 pixels or units per second
The average velocity is 90° at 8 pixels or units per second
Example 3
Velocity 1 is 0° at 10 pixels or units per second
Velocity 2 is 90° at 10 pixels or units per second
The average velocity is 45° at 14.142 pixels or units per second
I am using JavaScript but it's mostly a language-independent question and I can convert it to JavaScript if necessary.
If you're going to be using a bunch of angles, I would just calculate each speed,
vx = v * cos(theta),
vy = v * sin(theta)
then sum the x velocities and the y velocities separately as vector components and divide by the total number of velocities,
sum(vx) / total v, sum(vy) / total v
and then finally calculate the final speed and direction with your final vx and vy. The magnitude of the speed can be found by a simple application of pythagorean theorem, and then final angle should just be tan-1(y/x).
Per example #3
vx = 10 * cos(90) + 10 * cos(0) = 10,
vy = 10 * sin(90) + 10 * sin(0) = 10
so, tan-1(10/10) = tan-1(1) = 45
then a final magnitude of sqrt(10^2 + 10^2) = 14.142
These are vectors, and you should use vector addition to add them. So right and up are positive, while left and down are negative.
Add your left-to-right vectors (x axis).
Example 1 = -10+5 = -5
Example 2 = -8 = -8
Example 3 = 10 = 10. (90 degrees is generally 90 degrees to the right)
Add you ups and downs similarly and you get these velocities, your left-to-right on the left in the brackets, and your up-to-down on the right.
(-5, 0)
(-8,0)
(10, 10)
These vectors contain all the information you need to plot the motion of an object, you do not need to calculate angles to plot the motion of the object. If for some reason you would rather use speeds (similar to velocity, but different) and angles, then you must first calculate the vectors as above and then use the Pythagorean theorem to find the speed and simple trigonometry to get the angle. Something like this:
var speed = Math.sqrt(x * x + y * y);
var tangeant = y / x;
var angleRadians = Math.atan(tangeant);
var angleDegrees = angleRadians * (180 / Math.PI);
I'll warn you that you should probably talk to someone who know trigonometry and test this well. There is potential for misleading bugs in work like this.
From your examples it sounds like you want addition of 2-dimensional vectors, not averages.
E.g. example 2 can be represented as
(0,10) + (0,-10) + (-8, 0) = (-8,0)
The speed is then equal to the length of the vector:
sqrt(x^2+y^2)
To get average:
add each speed, and then divide by the number of speeds.
10mph + 20mph / 2 = 15
12mph + 14mph + 13mph + 16mph / 4 = 14 (13,75)
This is not so much average as it is just basic vector addition. You're finding multiple "pixel vectors" and adding them together. If you have a velocity vector of 2 pixels to the right, and 1 up, and you add it to a velocity vector of 3 pixels to the left and 2 down, you will get a velocity vector of 1 pixel left, and 1 down.
So the speed is defined by
pij = pixels going up or (-)down
pii = pixels going right or (-)left
speedi = pii1 + pii2 = 2-3 = -1 (1 pixel left)
speedj = pij1 + pij2 = 1-2 = -1 (1 pixel down)
From there, you need to decide which directions are positive, and which are negative. I recommend that left is negative, and down is negative (like a mathematical graph).
The angle of the vector, would be the arctan(speedj/speedi)
arctan(-1/-1) = 45 degrees