I posted this problem in another section, but it seems to have fizzled out and I’m trying to solve it, so resurrected it here hopefully to get somewhere.(adsbygoogle = window.adsbygoogle || []).push({});

I’m trying to calculate the impact force of a free falling cylinder of metal under water accounting for the drag. The cylinder is restricted to vertical falling, so cannot tumble down so to speak.

I started with the work energy principle and net work done to calculate the impact force, but now I am trying to include the drag from the water.

I got a couple of equations, one being stokes Fd = 6PIuvd and the other being Fd = 0.5CpAv^2.

Using the principle that the forces of buoyancy and drag are equal to the force of it falling; mg=Fb+Fd, I started to try and work things out.

Buoyancy force I used is the displaced fluid weight times the accel due to gravity. So here I used;

Fb = volume of cylinder X density of fluid X accel due to gravity = PIr^2hpg

For drag I used either Fd = 6PIuvd or Fd = 0.5CpAv^2 in each calculation.

I rewrote the equations with all the available parameters:

mg = PIr^2hpg + 6PIuvd

or

mg = PIr^2hg +0.5CpAv^2

I then rearranged for velocity, my objective is to isolate velocity inclusive of drag, then I can use that new calculated velocity in the original work energy principle and get the new impact force. So I get;

v = [ (m*g) – PI*r^2*h*p*g ] / 6*PI*u*d (eqn1).

Or

v = sqrt{ 2*[ (m*g) – PI*r^2*h*p*g ] / C*p*A } (eqn2).

I used the following for the parameters;

m = mass of metal cylinder, I used 10kg

g = acceleration due to gravity (9.8m/s^2)

PI = 3.1416

r = radius of cylinder, I used 7.5cm

h = height/length of cylinder, I used 30cm

p = density of fluid, I used 1000kg/m^3

u = viscosity of fluid, I used 0.00179 Pa.s

C = drag coefficient of cylinder, I used 0.82

d = diameter of cylinder, I used 15cm

A = cross sectional area of cylinder

Eqn1 doesn’t give me physically possible number as answer (>9k), eqn 2 could be, i.e. it’s less than 9.8, which I’d expect. Things fall slower under water than in air.

Am I going about it the right way, if not, where am I going wrong etc.

Thanks in advance for help/pointers etc.

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# Free fall velocity of object under water

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