So when you say acceleration is a function of position, are you saying F = ma = -kΔx (english language to math language is not my strong suit! Haha)? So would ak1 just be -kΔx/m? I think if I can get that relationship, I could figure out the implementation . . . I think
So in the example above, are you using the K values only on calculating acceleration? Then do you solve it like normal, or would you repeat that process for X and V, where V would be solved using K values? Cause the way I know it is that the K values are in the form h*f (where f is the multivar...
I'm not sure if this is the appropriate place, but I've just been searching, with no luck, on how to solve a spring system with RK4 (hence the math section, since it's a Runge Kutta question). How would you set it up to change position based on spring properties? I haven't really found any...
I found this Matlab code:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Program: blasius
%
% Solve the Blasius problem
% using 2nd order Runge-Kutta
%
% Mark Blyth 2007
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
close all
clc % Clears the command window
%%
% Set initial condition, step...
. . . Possibly I have learned that? . . .
So here's the equations for fj and gj we were given:
gj = [∆η2/4][2gj+1/∆η2 + 2gj-1/∆η2 + fj([gj+1-gj-1]/2∆η)]
fj = ∆η[fj-1/∆η + (gj+gj-1)/2] = fj-1 + ∆η(gj + gj-1)
So to solve that, do I need to put in random initial guess to help iterate through...
The B.C.'s we have are f(0) = 0, f'(0) = 0, and f'(∞) = 1, and that's directly relatable to η (so pretty much f(η), or at least that's what it looks like).
I guess that math sort of confuses me than. I'm looking at this without much going on upstairs. I have a whole bunch of letters, like f and...
1. Homework Statement
Program, without any built in functions (like ODE45), a solution to the Blasius Equation in Matlab that outputs boundary layer profiles for given x values, u values, etc.
2. Homework Equations
2f''' + f''f = 0
fj = fj-1 + Δη/2 * (gj + gj-1)
gj = [Δη2/4][2gj+1/Δη2 +...
So I'm gonna do it the capacitance way just 'cause that's what we have in our lecture notes (the brief brief notes).
I have the spring and mass 1 in series, and that series is in parallel with the second mass, which is in series with the current supply. So the laplace equations are something...
That's actually one of the website I used haha. So I guess now it's just making sure the circuit is correct. I have the force (current) in one loop that has the x2 node and m2 inductor. Then another loop which has the x2 and m2, a 1/k capacitor, and ends with an m1 inductor from the x1 node...
1. Homework Statement
Find the transfer function for the following mechanical system with force input fin and output x2.
2. Homework Equations
3. The Attempt at a Solution
The reason I left the equations blank is because I'm not sure how to appropriately model this scenario. I've seen two...
Woopsie, right. LC
Ok sweet, thanks. I just can't remember something we might have glossed over a few years ago . . . and no one recently has said "You can do this to a derivative". They just sorta do it on their own.
1. Homework Statement
Find a differential equation that describes the circuit that includes only vin and vout as variables.
2. Homework Equations
C(dvin - dvout)/dt = i
vin - vout = L(di/dt)
3. The Attempt at a Solution
So the answer I got was:
C(d2vout/dt2) + vout = LC(d2vin/dt2)
My...
So are you saying the CS integral will simply be ρV2A, and the other term will be ρV(dv/dt). Since you said a rate of change. And I don't know how to relate explicitly density and velocity to force
1. Homework Statement
As water flows through the pipe at a velocity of 5 m/s, it encounters the orifice plate, which has a hole in its center. The pressure at A is 255 kPa , and at B it is 180 kPa, Assume water is ideal fluid, that is, incompressible and frictionless. Determine the force the...
1. Homework Statement
The apparatus or "jet pump" used in an industrial plant is constructed by placing the tube within the pipe. The velocity of the flow within the 200-mm-diameter pipe is 2 m/s, and the velocity of the flow through the 20-mm-diameter tube is V = 37 m/s . The fluid is ethyl...
Wait . . . so are you saying to use ρAV2 to find the flow at the inlet and each outlet (but for the outlets, use the cos of half the angle)? And just take the difference of inlet/outlet flows as the force?
mass flow rate = ρVA = 62.4 * -12 * π(3/24)2
That's density times velocity dotted with the normal (that's why it's negative) times the area of the circle the water is traveling through.
Would it be constant over the diffuser, but different than the above calculation? Including the velocity? And...
1. Homework Statement
Water exits the 3-in.-diameter pipe at a velocity of 12 ft/s and is split by the wedge diffuser. Assume water is ideal fluid, that is, incompressible and frictionless. Determine the force the flow exerts on the diffuser. Take θ = 30 ∘
2. Homework Equations
F = ρAV
3...
Right right.
(1/30) x2 + x + C = ln(y)/2t
I plug in my initial x,y,t points:
0.2 + C/30 = 0.44794
Solving for C yields C = 7.4382
So now (and I'm going to just drop my thirty in the denominator):
(x2 + x + 7.4382)/30 = ln(y)/2t
(2tx2 + 2tx + 14.8764t)/30 = ln(y)
e(2tx2/30 + 2tx/30 +...
I divided the thirty into the dx equation.
So it's legal to set these equal to each other, put in the conditions, solve for the constant (which, now I understand why no one was putting in both C1 and C2), then rearrange to have y on one side and x on the other?
So:
dy/v = dy/2ty
dx/u = (1/30)(2x+1)dx
I get x2 + x + C1 and ln(y)/2t + C2
How do I solve for those constants to get y=f(x) form using the given boundaries?
Wait, that's what that letter means? So it's just ϒh + ϒh?
EDIT: Jeez that would have been helpful to know. Or know to infer . . . Yes, just do that to get psf and convert to psi to get the right answer . . . Wow. Thanks. But what about B? The only thing above B is air . . . and they don't give...
I'm trying to find gauge pressure at multiple points in a "mixed" container. Which, I thought would be equal to ρghliquid 1 + ρghliquid 2 etc. Well, that's not right? And I don't know why?
So for point A, I did: (55.1 * 32.1 * 4) + (62.4 *32.1 * 4). Then I divided by 144 to get it into psi. I...
1. Homework Statement
A fluid has velocity components of u=[30/(2x+1)]m/s and v=(2ty)m/s,where x and y are in meters and t is in seconds. Determine the equation of the streamline that passes through point (2 m, 6 m) at time t = 2 s. Write the equation in the form y={y(x)}m, where x is in...
r=ztanθ
Isn't velocity ωr? So ωztanθ?
I don't really understand that last points you made, but so far is this correct? I know the final answer has a sinθ in it, and it's because the thickness of the cone is used instead of height. But the reasoning behind the confuses me too . . .
Sorry, it's the terminology that's different.
I've been using compressed liquid, saturated mixtures, and superheated vapour tables, but the ammonia only has a Saturated table and Superheated table. That was the problem =\ But I think we got the appropriate interpolation now!