I am trying to calculate the equivalent length of a copper winding with several mitered joint extensions on both ends in order to divide it into equally flowing sections.

Through some searching online I found a site that lists Appendix A-29 from the Crane Flow of Fluids paper. I've seen some other calculations online that use just the number in the K coefficient to calculate the equivalent length of fittings and bends. So my question is should I use the formula KB = (n - 1)(0.25pi fT r/d + .5K) + K to calculate the equivalent length of the coil section since it is a series of 90 degree bends?

My thought is, if you just use the number in the K coefficient, then giving that a value of x in the above formula you can factor out the fT and get:

(L/D)eq = (n - 1) (.25pi r/d + .5x) + x

My math so far for this is as follows, any help on everything I am wrong on would be appreciated:

Copper size = .5" X .75" X .100" wall tube = .3 X .55 inside dimensions

Equivalent Diameter = 4A / P = 4*.3*.55/(.3+.3+.55+.55) = .3882

(L/D)eq for mitered 90 = 60

Leq = 60 * .3882 = 23.2941

winding r/d = 3.625/.3882 = 9.337

(L/D)eq for 10 = 30

(L/D)eq = (60 - 1) (.25pi * 3.625/.3882 + .5 * 30) + 30

(L/D)eq = 1347.6681

Leq = 2645.6725 * .3882 = 523.2123

Segments:

2", mitered 90, 4", mitered 90, 2", mitered 90, 3", mitered 90, 26", mitered 90, 2", mitered 90, 2", 60 turn coil, 2", mitered 90, 2", mitered 90, 26", mitered 90, 3", mitered 90, 2" mitered 90, 4" mitered 90, 2"

12 mitered Joints = 23.292 * 12 = 279.5294

82" of straight length

523.2123 Winding Equivalent Length

Total Equivalent Length = 885" ]]>

Is it worth me trying to understand some basic concepts about this now or do I really need "to climb the tensor mountain" to get there? Or can I do some "good enough" analysis with just some vector calculus and linear algebra?

I am basically trying to understand why, in rotating polar co-ordinates, that the circumference undergoes fitzgerald contraction but the radius does not and whether it annihilates the minkowski flat space-time assumption. ]]>

It shows a couple of box cars going through a tunnel which ar attached together (not shown). However when the wheels are placed over two sensors simultaneously (shown as yellow triangles) a light bulb turns on. If only one of the sensors is activated the light bulb will not turn on. Now if the box cars are stationary and placed as in the diagram the light bulb will turn on.

However, now for the tricky part. If the box cars are move close to the speed of light and travelling through the tunnel and they are length contracted the wheels will never simultaneously touch the sensors. Will the light bulb ever turn on in this scenario, for the briefest of time, or does the fitzgerald contraction of SR prevent this from happening?

What makes this even more fun is that a passenger in the box car sees the railway lines contracted instead so he sees the sensors as closer together. At just the right speed the sensor will be close enough together so that they will be both under the wheels of the first box car. (3rd picture). In this scenario the light bulb would turn on ... or would it?

here's an example. i need to be able to see the workings too so that I can work through similar problems please.

What mass could be hung from the swing if the diameter of the cable was 8mm?

Can you help please? just don't know where to start. Its been 30 years since high school and I just need a hand to get through some of these problems to get back on track. I have a few more that I need help with but just trying to take it one at a time!

To work this out we need to understand the force and stress applied?

So i Think I need these two formulas but what's next?

Force = mass x gravity

F = mg, where F is force (Newtons), m = mass (kg) and g = acceleration due to gravity (9.8ms-2)

We know the mass so we flip the equation

m = 750 x106 / 9.8ms-2

Stress = Force / Area

Am I anywhere close? here's another one

Calculate the height of the shelf using the displacement/velocity/acceleration equation.

The package is stationary so its acceleration is zero. Two forces are in play, the force from table pushing upwards (normal force) and gravitational force pushing downwards which are equal so net force is zero.

The formula to work out the displacement (distance) is s = ut + ½ at2[1] where s is displacement, u = initial velocity, t = time, and a = acceleration.

s = (0 x 7.5m/s) + ½ x acceleration x 7.5m/s2

Any help apprecaited!

nd another

3. Propane gas is leaking from a cylinder in the immediate vicinity of an insulated conveyor belt which has built up a charge of 2.5μC. If the conveyor belt has a capacitance of 80pF, is there a danger of the propane being ignited? Consider both electrical energy and voltage in your answer.

here;s what i have so far - am I anywhere close? Not even sure how to lay out the answer. have done my best

Capacitance

Charge can be stored on an object that has capacitance which in this case is 80pF.

80pF = .8 x 10-10

= 0.00000000008F

Charge

Now Charge (Q) in Coulombs is 2.5μC = 2.5 x 10-6C or 2.5 x 10-8C

V = Q/C where C is the capacitance (in Farads - F) and Q is the Charge (in Coulombs)

Since V = Q/C the voltage is:

V = 2.5 x 10-8 / .8 x 10-10

= 0.000000025 / 0.00000000008

= 312.5 V

A charge q which is at a voltage of V volts, has an electrical potential energy W = qV.

W = qV

= (2.5 x 10-8) x 312.5

= 0.000000025 x 312.5

= 0.0000078125

= 7.81 x10-6

= 7.81mJ

Minimum ignition energy in air for acetylene is around 17 mJ . In this case there is little danger of the acetylene being ignited from the electrical potential energy.

Voltage risk of ignition/explosion???? Can you please direct me in any way?

here's what I have - anything right here lol?

“To reduce the dose rate by a factor of 4 then the distance to the source must be doubled”[p.18, 3]

The distance if multiplied by three reduces the dose rate to 1/32, the distance multiplied by four reduces the dose rate to 1/42 and so on. So at 6m, five times the original distance (5 x 1.2m), the dose rate has reduced to 1/52 or 1/25 of its original value.

Distance (m) from source Multiplier Dose rate

1.2 1 Original value

2.4 2 ¼ of original value

3.6 3 1/9 of original value

4.8 4 1/16 of original value

6 5 1/25 of original value

12 10 1/100 of original value

The dose rate above is proportional to the inverse square law 1/d2 where d = distance to the source.[3]

Position 1: 1/1.22

=69.4%

Position 2: 1/62

=2.78%

Percentage reduction from position 1 at 1.2m to position 2 at 6m = 66.6%. (is this right?)

here's what I have so far - anything right here?

For Joan to be able to move the box the force applied to the box, F, must be greater than fmax = μ W[4].

W = mg

= 50 kg x 9.8 ms-2

= 490 Newtons (N).

If CoF [μ] = F/N, where F = horizontal force required to slide a mass across a surface and N = normal (i.e. vertical) force being exerted on the surface by the object, and if Joan can only apply a maximum force of 150N, then the CoF [μ] would need to be a maximum of 0.3 for her to still be able to move the box slightly.

F > 0.3 x 490 = 147N

Q The next day Joan decides to sweep the floor before trying to move the next box, but she finds that she can’t. What might be the reason?

Perhaps the lower frictional resistance available for Joan herself due to less dust on the floor (causing slipping), or in other words the “lateral force applied at the foot-surface is greater than the frictional resistance available”[p.4,4], no longer allows her to apply 150N force or the reduced force now necessary to move the box.

ANY HELP APPRECIATED! ]]>

I came across a problem recently which, in hindsight I believe I do not fully understand, and as a consequence of this I cannot seem to get the correct solution no matter how I tackle it. As I have gone through several different attempted solutions to the problem I will just list below the problem and my most recent attempted solution, and would appreciate it if someone could point me in the right direction as to how to solve the thing.

You hang a

Now I started off with the above equation then I assumed that the thin hoop corresponds to the same shape as a

Now since the pivot point of the new axis (the nail) is at the rim of the hoop then the value of 'd' (distance of new axis to centre of mass axis) in the original equation is equal to the radius of the hoop (R) .

If we then substitute these values into the equation above we get

I we then apply the energy equations to this system we have ..

where K (i), K (f) are initial and final kinetic energy values and

U (i), U (f) are initial and final potential energy values

Now K (i) and U(f) are both zero

and

and

So we now have ..

Giving ...

so

However the answer the book gives form this problem is ..

I don't understand this answer and don't know where i have gone wrong, can anyone help ?

Regards,

Jackthehat ]]>

I try to calculate the coefficient of pressure drop in rectangular conduit which contains 6 "U" shaped air heating elements", as shown in the following figures:

Any help would be much appreciated!! :)

If the two manipulators move apart in x direction within the same force and the same distance, the forces applied to the point in the panel will be the opposite to each other and will be cancelled out. So then the panel will be stay where it was? But I feel like the panel will move downward when the two manipulators move apart though. I need theoretical explanation what will happen to the panel when two manipulators move apart in x direction. Any ideas?

If I had an imaging system in a black box, how could I derive its response function?

My first idea was to use a plane wave, and measure the output. I know that the convolution of the input wave with the response function gives us the output. As we know the input, could we just measure the output to derive the response function?

It seems to easy to me but I'm not sure what else I could do. I could measure the intensity of the outgoing wave, but does that necessarily let me derive what the original wave looked like?

All my textbooks work the other way, they begin knowing the response function to derive a function for the output. ]]>

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But the what is the exact meaning of Euler's number in electromagnetism? How exactly it is used in electromagnetism? And how come it is so necessary?

I need very illustrative and INTUITIVE understanding about the use of

I'll be thankful for every reply.... ]]>