But if there will be a phase change, additional energy will be required to rise through the temperature of the liquid to gas transition. The specific heat will differ for the liquid and gas phases.
I have not yet looked at your revision, but the agreement between our numbers was close to numerically perfect.
Pitch angle 33.995 °
Torque at a = 45°, 0.835437 Nm
alpha Baluncore JBA difference
90.0 1.#NAN00000 1.181486720 % 1.$E+00
85.0 1.#NAN00000 1.176990806 % 1.$E+00
With LTspice you can examine the frequency spectrum of the output signal.
Select the time plot of the signal you want to analyse, then the view menu, select FFT.
I see your three sinewave signals without any modulation.
Water hammer is a transmission line effect. The liquid is not compressible.
A shock wave pressure step compresses and heats a gas, which increases the speed of sound behind the step, so it accelerates the velocity of the shock front and keeps the step sharp.
If you know the mass and properties of the liquid, you can deliver sufficient energy to vaporise the liquid. The evaporating liquid will cool the heating element until all is evaporated, when the temperature of the heating element will rise suddenly.
We still have no idea of the scale. Is it...
I believe you are seeing the momentum of the gas flow in the inlet and exhaust ports.
The induction stroke starts out drawing air through the inlet port into the cylinder. The velocity rises at first but when the piston slows down there is an over-pressure due to the momentum of the induced...
Decades ago, I looked at the possibility of moulds made from a bed of close packed hexagonal pins, covered by a sheet of rubber, all held down by a vacuum. The aim was to select, place and adjust the pins automatically from a numerical definition of the surface.
When it comes to metals and their alloys, if you look at an alloy phase diagram you will see that the highest temperature is one of the elements, with the lowest temperature being the eutectic alloy.
That suggests it is most unlikely there will be a higher melting point alloy than one of its...
Will there actually be a “shock wave” ?
The speed of sound is 5,130 m/s in iron, but only 1,450 m/s in mercury. The pressure step that starts in the mercury will gradually enter the iron and race ahead of the pulse that remains in the mercury. Some of that energy will reenter the mercury well...
The resistance of a pure metal like copper is proportional to absolute temperature.
What are the dimensions of the wire, and will you heat it with AC or DC current.
What are you trying to do with the hot wire.
There may be a better solution if we knew the application.
I am no conquering mathematician, I just crunch numbers. If I was any good at math then perhaps I would have recognised my ratio of kb/ka contained Sin(a)/Cos(a) = the Tan(a) function and that it too might cancel the Asin() and collapse to your simpler solution. Trigonometric identities never...
When I collapse your energy method equations to eliminate common factors and temporary variables, I get, using my variable names;
Torque = m * g * Sin( a ) * p / ( 2 * Pi );
Note that, as I expected, the number of turns and the radius do not appear in the calculation.
That is the...
@JBA. Well done.
I think our methods give the same results up until the minimum disappears at alpha = 90° – pitch angle.
I believe the energy method should work because applying a fixed helix torque to counter the torque induced by the ball on the helix will hold the ball in position, with no...
LTspice models voltage sources as having Rser = zero, unless you specify otherwise.
The source resistance of the three perfect voltage sources in series is zero.
The amplitude of the output voltage will halve when the load resistance is equal to the source resistance. When I change the load...
In post #84 I gave the 4 steps needed to calculate the torque on the helix due to a ball.
Then in post #88 I gave my full derivation of the method. So others may compare their results.
You do not need to understand the full derivation. Do the calculation in post #84.
You have significant input current so you need to match the source impedance of the (–) and (+) inputs. The op-amp output can be seen as having a low impedance.
So with Rf = 100k, and R = 11k11, the source impedance on the (–) input will be Rf in parallel with
R, giving 10k0. To avoid offset...
50 volts is too high for the majority of buck converters.
You must find one that will work safely at higher voltages, or use a pre-regulator to drop the converter input voltage to safe levels.
Buck converters can be very efficient. A divider or series resistor to drop voltage before the buck...
Here is my derivation of the equation for torque due to a ball in a helical tube.
I believe this follows a similar method to Daniel Bernoulli in 1738.
We start by defining a filamentary helix wound on a cylinder of radius, r.
The advance per turn of the helix is the pitch, p.
The bottom of the...
This week SOFIA will be on display in Stuttgart where around 400 researchers from all over the world come together for a major conference of the Astronomical Society at Stuttgart University, celebrating the centenary of the International Astronomical Union.
The first observation mission over...
It should not be so obvious that my result is correct.
Finding the position of the minimum on the helix turn is necessary. I wrote the equation for the height of the helical filament, then took the derivative of that and solved it for zero. The position of the second zero is the minimum.
Here is my minimum solution. The derivation of this is a little longer.
First Specify Helix and Ball Parameters.
d = 45 ' tilt of helix axis above horizonal in degrees
r = 0.059 ' radius of helix cylinder, metre
p = 0.250 ' pitch, helix advance per turn, metre
m = 3.030 ' mass of ball in kg...
Live, neutral and ground suggests the MEN system, not a balanced supply with two half voltage active lines such as used in USA.
In Multiple Earthed Neutral (MEN), the neutral is earthed at each consumer service point.
@JBA I have some doubts about your numbers, the reason being that your value for torque falls smoothly to zero as the available minimum, that holds the ball, ceases to exist at alpha = (90 – beta).
You specify alpha as helix axis angle measured from the horizontal, but then tabulate from 90...
Don't forget that conservation of energy limits the rise possible and that friction must result in an overall loss of potential energy. Perpetual motion and over-unity efficiency are clearly not possible.
In the MEN system the voltage on the active and neutral is asymmetric as the neutral is earthed at one point in the breaker/distribution box. The earth wire lies with neutral and active in the same long cable bundle and so forms a three way capacitive divider. The small capacitive reactive...