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Help with some maths Please?

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john_1
Super Contributor
Hi guys I need some help...I need to work out the volume of a cylinder. If the cylinder has length of 60 mm and a diameter of 8mm what is the cylinders volume... Now if I shorten the cylinder to 45mm how big do I need to make the dimeter to have the same volume... thanks in advance John
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47 REPLIES 47
Not applicable
John, formula is

How to Measure a Cylinder

Radius=r

pi = 3.14259 (approx.)

Area=A

Height=h

Volume=v

First calculate the area of the circle: A=pi*r*r

Then multiply by the height to attain volume: v = A*h = pi*r*r*h

in your case the volume will be = 3017.1428571428546 cubic mm

I am sure you can play with the formula to see what diameter you will need for 45 mm height. But my best (closest) calculation will be about 9.24mm
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duke_vest
Frequent Contributor
john u doing a gr 9 maths examination?
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Wizard
Super Contributor
That sounds like a bottle of wine that John is redesigning. I like the idea John, hope u choose a good color!
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Wizard
Super Contributor
It's too small...Small bottle of whiskey then.
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Terra
Super Contributor
CPS your answer is correct.
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john_1
Super Contributor
Thanks Very Much Guys This is very helpfull.
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Not applicable
If volume is 3017 and height is 45 then pi x r x r x 45 = 3017 Therefore r x r = 3017 divided by (pi x 45) Take square root to find r Multiply by 2 to find diameter
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Starsky
Frequent Contributor
take note that the optimal diameter and height will require 2nd derivative calcualtions. regards
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Not applicable
And check the moody diagram to calculate pressure drop IN THE cylinder as a result of pipe friction. tip : first determine relative pipe roughness aND determine the reynolds number and the check whether flow is laminar or turbulent ie Re > 2000 then turbelnt. then check if pipe wall thickness is sufficient by using basic formula: stress = pr/t.(p=pressure, r=pipe radius, t= wall thickness) and check max allow tensile stress for the used material. and If using as a pressure vessel, hydrotest 1.5 times max allow P. _____hope this helps
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r_n
Contributor
Take note however that if the bottle is not stationary then it might also be necessary to consider the length dilation that is likely to occur. The length of the bottle in a moving frame will appear somewhat shortened in the direction of motion. The amount of contraction can be found by using the Lorentz transformation. The length is at its max in the frame in which the object is stationary. L = L0 * sqrt((1 - (V^2)/(C^2))) ..where L0 is the length measured in the moving ref, v its velocity and c the speed of light in a vacuum.
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Not applicable
So if avail space is the limiting factor, it might be an option to make the cyl travel 0.8 times the speed of light for it to contract and fit. but this is merely an optical illusion. extending the tube and using a smaller diameter would be recomended
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Wizard
Super Contributor
I can't believe this...You forgot to add a pump into the system. Make sure it uses the correct Operating point and it can handle corrosive liquids because u never know what will go through it
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Wizard
Super Contributor
That is the equation I use to make me rich! Can't go wrong with it! ;)
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dilligaff
Super Contributor
Starts to hum
An engineer told me before he died uh hum, uh hum.....
He knew a cylinder that was so wide, uh hum, uh hum ...
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barry_1
Super Contributor
at this moment i'm kinda glad,i've invented nuthin!
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r_n
Contributor
The LHC (large hadron collider) should be used to test the observability of this dilation effect as the use of gyrogroup theoretic techniques have been found to support the original hypothesis
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kwagga
Super Contributor
This is the most interesting thread in two weeks. Just goes to show that markets has become a little boring and lacklustre recently.
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Not applicable
Judging by the size of the tube, I presume john is using it as a stabilizing cappilirary tube used for cooling, used in his experiment to observe the circular movements of accelerated elecros in an ideal gas enviroment caused by the two poles of a magnetic field acting diagonally across the path of projected motion. If subject to high loads, the induced vibration can be minimized by countering the simple harmonic motion by means of a fourier sequence calculation. It involves integration techniques, int-by-parts inclusive. Sbk doesnt provide a mathematical platform for me to submit the required calculations and formulae. sadly
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Wizard
Super Contributor
You are...The `Chartist' of Physics!!! :)
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