What is terminal velocity formula -Terminal velocity of body falling through a viscous fluid derived

this video reveals what the terminal velocity formula is by deriving it. to support the production of this work, please Consider Funding me via   / kisemboacademy  . Terminal velocity of body falling through a viscous fluid derived in this video i get to derive the expression for terminal velocity of a body falling through a viscous fluid. #terminalVelocity #Viscosity #FluidMechanics transcript; in this video we get to discuss the vertical motion of a body when it is falling through a viscous fluid right there we have a data that is describing the solid sphere this solid sphere is 0:00:17.789,0:00:21.960 falling through what we call a viscous 0:00:19.770,0:00:22.949 fluid this viscous fluid could be 0:00:21.960,0:00:26.099 porridge 0:00:22.949,0:00:29.220 it could be glue it could be engine oil 0:00:26.099,0:00:32.040 does fluids that I think those are the 0:00:29.220,0:00:32.790 viscous fluids the ones that are hard to penetrate because of their viscosity and thickness so now this body when it is falling 0:00:37.920,0:00:42.950 through the viscous fluid there are some 0:00:39.690,0:00:47.489 forces that are acting on this sphere 0:00:42.950,0:00:50.219 these forces are the upthrust force that 0:00:47.489,0:00:52.350 is derived from a Smithy's principle we 0:00:50.219,0:00:54.809 also have this force capital F called 0:00:52.350,0:00:57.539 the viscous drag the one that we 0:00:54.809,0:01:01.050 discussed in a previous session where we 0:00:57.539,0:01:02.789 had the basis for Stokes flow and that 0:01:01.050,0:01:05.880 then also we have the force that is 0:01:02.789,0:01:08.189 making this fold down in the liquid and 0:01:05.880,0:01:11.820 that force is what we are calling the 0:01:08.189,0:01:13.799 weight of this sphere the weight that is 0:01:11.820,0:01:15.990 propelling this fear to fall through 0:01:13.799,0:01:18.479 this viscous fluid so we have these 0:01:15.990,0:01:22.680 three forces we have this was down and 0:01:18.479,0:01:26.960 these two forces up now we assume that 0:01:22.680,0:01:29.970 this this sphere is falling through this 0:01:26.960,0:01:32.729 let's call let's assume this thing is 0:01:29.970,0:01:35.820 very tall and it's falling through a 0:01:32.729,0:01:39.270 very tall jar that is full of engine oil 0:01:35.820,0:01:42.869 for example so at the beginning this 0:01:39.270,0:01:45.210 weight is bigger or it is it is bigger 0:01:42.869,0:01:47.310 than these two forces combined in other 0:01:45.210,0:01:49.470 words the downward forces are bigger 0:01:47.310,0:01:51.869 than the upward forces and because the 0:01:49.470,0:01:54.630 downward force is bigger than the upward 0:01:51.869,0:01:58.170 force therefore there is an acceleration 0:01:54.630,0:02:02.460 as this sphere is dropping down the 0:01:58.170,0:02:04.740 fluid but after some time it's going to 0:02:02.460,0:02:08.190 happen in such a way that as this thing 0:02:04.740,0:02:11.129 goes down the downward forces are going 0:02:08.190,0:02:13.590 to be equal to the upward forces that 0:02:11.129,0:02:15.870 happens because this vehicle 0:02:13.590,0:02:18.060 used to go down the viscous drug keeps 0:02:15.870,0:02:20.459 increasing remember cording to stop slow 0:02:18.060,0:02:23.250 that as the velocity of this thing keeps 0:02:20.459,0:02:24.330 increasing because it is the velocity 0:02:23.250,0:02:26.940 keeps increasing 0:02:24.330,0:02:28.590 so as the velocity keeps increasing the 0:02:26.940,0:02:31.709 viscous drugs also keeps increasing 0:02:28.590,0:02:33.540 because the viscous drag if and the 0:02:31.709,0:02:36.450 velocity those two are directly 0:02:33.540,0:02:38.819 proportional according to stock we'd 0:02:36.450,0:02:42.150 covered that in the previous session so 0:02:38.819,0:02:44.160 as that continues this ball continues to 0:02:42.150,0:02:46.799 fall through this viscous drug the 0:02:44.160,0:02:49.319 downward forces eventually equalize with 0:02:46.799,0:02:52.349 the upward forces and now when the 0:02:49.319,0:02:55.079 downward forces equate or are now equal 0:02:52.349,0:02:59.190 to the upward forces you realize that 0:02:55.079,0:03:01.950 now this body or this fear stops 0:02:59.190,0:03:06.420 accelerating and so it starts moving at 0:03:01.950,0:03:07.860 a certain constant velocity now when it 0:03:06.420,0:03:10.470 starts moving at a constant velocity 0:03:07.860,0:03:12.900 because now there's no more acceleration 0:03:10.470,0:03:14.940 the resultant force on this thing is now 0:03:12.900,0:03:17.190 zero since the upward forces are now 0:03:14.940,0:03:19.139 equal to the downward forces that 0:03:17.190,0:03:22.260 velocity it will have attained is what 0:03:19.139,0:03:23.910 we call the terminal velocity so if I 0:03:22.260,0:03:26.970 may define what terminal velocity is 0:03:23.910,0:03:29.519 recon say that terminal velocity is the 0:03:26.970,0:03:31.829 #Physicsmaths