Mechanical Properties of Fluids | Full Marathon & PYQ's | RE- NEET 2026 Revision Series | Siva sir

Added: 2026-05-23

[00:00:05]Okay.

[00:00:10]So chapter successful gravity and solids fluid mechanics.

[00:00:23]Right.

[00:00:32]And regarding fluid mechanics it can be difficult just basic final formula most of the complicated in-depth problems I mean usually it will be like shallow formula application solution Done.

[00:01:00]Right. So first question.

[00:01:05]So fluid mechanics formula pressure force by area thrust by area. So thrust force perpendicular perpendicular to the surface surface.

[00:01:41]pressure.

[00:01:51]the force by area and the unit obviously newton per meter square.

[00:02:03]So fluidsity density and obviously and kilogram traditional formula fluid pressure fluid Pressure row G H Pressure exerted by a fluid is row G row density G acceleration due to gravity H height height height of the liquid column reference The idea is same water right formula is sorry unit is pascal Gauge pressure. This is fluid pressure.

[00:03:35]But particular pressure absolute pressure.

[00:03:42]Absolute pressure is atmospheric pressure plus P gauge pressure. So gauge pressure under a certain pressure. Correct. Deep space that is vacuumosphere let's say.

[00:04:19]Imagine.

[00:04:24]Yes.

[00:04:30]is so we are subjected to an ocean and ocean pressure right okay we are subjected to pressure exerted by an ocean filled with air and that's the idea Pressure in the gauge pressure absolute pressure atmosphere plus gauge.

[00:05:19]So atmosphere gauge pressure absolute pressure right. So for the gauge pressure g atmospheric pressure standard 10^ 5132 inspired by yes nice to meet you one sec.

[00:05:52]H.

[00:05:54]So absolute pressure gauge pressure right. So principle principle.

[00:06:11]So in the principle order formula upward force buoyant force buoyancy magnitude density of the liquid into volume of the solid but immersed part into g acceleration due to gravity is principid fully immersed on the density of the liquid or fluid whatever volume of the solid part into acceleration due to gravity row v right so buoyancy formula principle buoyancy formula done let's do Pascal's law pascal's law pascal's law statement fluid pressure will be evenly distributed throughout the liquid.

[00:07:23]Excess pressure.

[00:07:25]This is hydraulic lift and formula.

[00:07:35]You apply f_sub_1 in the area a1. Okay, you will get f_sub_2 in the area a2.

[00:07:42]Right? So f_sub_1 by f_sub_2 a1 equals f_sub_2 by a2. So usually area_2 will be greater than greater than area 1. Area you'll get f_sub_2 greater than greater than f_sub_1.

[00:08:01]So this is uh h pascal's law. So where an argument is principle.

[00:08:08]One sec.

[00:08:36]Next uh continuity equation.

[00:08:45]Continuity equation fluid flow. This is A2.

[00:08:52]This is A1.

[00:08:55]Fluid velocity V1. V_sub_2 then A1 V_sub_1 equals A2 V_sub_2 the continuity equation for any two cross-sectional areas area into velocity product is constant just the final formula area into velocity will be constant continuity equation next equation right so Bernoli's equation India random shaped pipe.

[00:09:31]Right. So equation P1 + half row V1² plus row G H1 equals P2 plus I I mean this is constant equation half row V_sub_2 squared plus G H2. So what are the values? Pressure P1 pressure P2 H2 even height H1 enter velocity V_sub_1 exit velocity V_sub_2.

[00:10:10]So fluid flow we can solve the entire stuff.

[00:10:18]Foreign cell equation to cell is equation.

[00:11:04]Heloc Val <unk>2 GH we call it velocity of flex right. So only the height velocity where factor of course you have g that is constant but height of the liquid flex velocity factor velocity of flex torsel is equation stokes law stokes law stokes law f= 6 pi r into e v right so the normal basic law viscous force spherical body of radius of viscosity force opposite direction velocity It's understood and this is Stoke's law and Stokes terminal velocity formula terminal velocity V_T is equal to 2 by 9 R² row minus sigma g by ea right so r² again on the body order radius row and sigma row density of the solid sigma density of the fluid coefficient of viscosity viscosity but this is the terminal velocity formula solid body of radius r or sperical solid body of radius r or fluid velocity downward force, gravitational force upward viscous force and buoyant force random equal and opposite velocity constant and that is terminal velocity and terminal velocity formula 2 by 9 r²ig by einal velocity formula for Yes. Po s e u i l l e u i l l e pois equation.

[00:14:25]So pi p r power 4 by 8 l right. So fluid flow rate of fluid flow again pressure difference pressure difference obviously of viscosity length of the tube. So rate of fluid flow po's equation I think yes major and one more one more one more reenol's number reynol's number r is equal to row v d by ea right so again row density of the liquid v velocity d characteristic dimension tube It depends mostly numbers dimensionless number is laminar flow 2000 flow 2000 it is transient flow right so three types of flows number we'll go to viscosity viscosity viscosity basic concept viscous force viscosity concept layers and layers like A4 sheets A4 sheets layers flow layer Opposition resistance like frictionid like when you rub two solid surfaces force liquid surface liquid surface one liquid layer resistance force Viscosity the resistance offered by a fluid to its own flow. Viscity the concept of viscosity viscous force the viscous force formula dv by dy. So dv by dy velocity gradient fluid flow right. So this is how it will be top velocity max velocity.

[00:17:55]So in the change in velocity in the dimension of y in the change in velocity actually this will be dv and this will be dy in the cross-sectional area. So f is equal to e by dc conceptual formula for r it's a right formula force is coefficient of viscosity coefficient of viscosity S unit Pascal Pascal second or CGS unit right okay viscosity quotient of viscosity yes done let's do surface tension surface tension they'll use a yes or t right so in the first letter yes the first letter t that's fine you can use that surface tension formulas force per unit length energy per unit area.

[00:19:43]This is a liquid surface in the surface divided by the length. So liquid length that is surface tension simple free surface freech property liquid free surface. Okay. So property surface tension.

[00:20:43]So it will try to shrink in return force per unit length. imaginary by the length, right? So surface tension is force per unit energy per unit area.

[00:21:25]So per change in area right and newton per meter per me² right most we'll stick to newton per meter is a surface tension of formula right next excess pressure and I go to liquid drop and air bubble.

[00:21:54]The air bubble inside water, right? Liquid drop and air bubble inside water excess pressure P inside minus P outside is equal to 2T by R. Right? Other way if I have a soap bubble film bubble pressure P inside minus P outside is equal to 4T by R. Obviously, surface rainface.

[00:22:54]So there are two surfaces two times. So 2T by Right.

[00:23:31]question.

[00:23:35]Right. Surface tension excess pressure.

[00:23:38]So bubble liquid drop.

[00:23:43]Yeah. Capillary rise.

[00:23:48]Capillary rul cos theta by row rgap.

[00:24:09]Right. So capillary formula. What else?

[00:24:34]I think that's it. problem starts.

[00:24:43]We did almost all the formulas equation equation important force formulas. Yes, we'll go to problems problems.

[00:25:07]problem. A submarine is designed to withstand an absolute pressure. Note this point your honor. Absolute pressure of 100 atmospheres. How deep can it go below the water surface? Consider the density of water th00and and atmospheric pressure 1 into 10^ 5 and gravitation 10. Right? So 100 atmospheric pressure atmosphere.

[00:25:43]Come on, let's do this.

[00:25:49]Atmospheric pressure gauge pressure liquid pressure absolute pressure 100 one atmosphere value 100 atmosphere 100 into 10^ 5 equals 1 atmosphere. So 1 into 10 ^ 5 plus liquid pressure row g h right pressure x liquid is g h substituteus 99 into 10^ 5 is equal to,000 into 10 into h, 10 h. So sol. So 1 2 3 4 like four. So 990 m approximately hydrostatic pressure 100 atmosphere 1009 cm. So 100 times will be crushed implosion.

[00:27:26]But submersible.

[00:27:40]Submersible.

[00:27:43]thick sheet metal submersible pressure but submersible.

[00:28:12]Okay, this is unnecessary information anyways.

[00:28:20]Right. An ideal fluid is flowing in a non-uniform cross-sectional tube XY as shown in the figure from end X to Y.

[00:28:29]Right? X Y. If k1 and k2 are the kindinetic energy per unit volume of the fluid at x and y respectively then the correct option is so either k1 and this is k2 k1 half m vx² velocity vx m v y² okay x and y 1 and V1² V2 squ this is let's say A1 and V2 and the area is A2 continent equation A1 A1 V1 equals A2 V2 up A let's do the ratio A1 by A2 is V_sub_2 by V_sub_1 A1 is less than A2. So as you can see V_sub_2 is less than V_sub_1 kinetic energy at 2 is less thaninetic energy at oneinetic energy one is greater than K2inetic two because they didn't give anything about the area we cannot say anything about B so answer is option Question C. One kinetic energy will be greater than the second kinetic energy.

[00:30:16]Right. The question a thin flat circular disc of radius 4.5 cm is placed gently over the surface of water.

[00:30:34]Okay. Surface tension 0.07 07 meter and the excess force required to take away take it away from the surface surface tension basgal It can be a curved line.

[00:31:19]circular flat discound.

[00:31:44]That is not a free surface, right?

[00:31:48]Top top view.

[00:31:51]If you look at it from the front, I hope you can understand this.

[00:32:08]Okay.

[00:32:15]2 pi r. So surface tension into 2 pi r will give me the total force t into 2 pi reng circumference is equal to f surface tension value 0.07 07 into 2 into 22 by 7 into radius value is 4.5 cm 4.5 into 10^ -3 10 newton per meter right soloma this and this 01 so yeah so 22 into 2 44 44 into 4.54 So numbers okay let's do the math 44 into 4.5 44 into 4.5 198 so 198 into 10 ^ -3 - 5 Newton so -5 five.

[00:33:32]So that would be calculation.

[00:33:59]1* 2 0.07 corrected into 2 pi rat 4.5 cm 10^us 3 my mistake forgive me 10 to the power -2 0.01 01 - 4 which is 19.8 into 10^ -3 which is 19.8 millton done 19.8 m. Okay. Yes. C see yes J&T forgive me. Please accept my sincere apologies.

[00:34:45]I mean option, right? Next question.

[00:34:55]Which of the following statement is not true? Coicient of viscosity is a scalar quantity. Of course, it is true. Viscous force coefficient of viscosity coefficient of viscosity is absolutely scalar quantity. Surface tension is a scalar quantity. Again you see surface tension is force per unit length.

[00:35:19]Yes it is a scalar quantity. So this true pressure is a vectority.

[00:35:27]Pressure is a scalar. So question which of the statement is not true? Third statement not true. And relative density as the density of a substance by density of water it is scalar quantity time right the viscous drag acting on a metal sphere of diameter 1 mm falling through a fluid of viscosity8 viscosity I mean it can mean different represents velocity velocity 2 m force. So in Stoke's law formula F is equal to 6 pi r into e v. So 6 into 22 by 7 into radius 1 diameter is 1 mm. Our radius would be diameter by 2.

[00:36:40]So 10^ -3 by 2 into cofficient of viscosity 0.8 into velocity 2 m/s. This this gets cancelled 22 by 7 first. options.

[00:37:02]Let us see 22 into we'll take it as 3.14 3.14.

[00:37:15]Okay. So 6 3es are 18.

[00:37:20]So around 1928 228.

[00:37:25]Okay. Answer either 15 or 1.5. No. So we'll do the math. 6 3 are 18 19 20 8 into 16. So this would be 18.8 18.8 around 16 into 10^ -3 Newton rough when I do the rough math rough mathematics.

[00:37:58]This is what you should get. Closest to possible option is 15 into 10^8.

[00:38:07]I'm making a mistake somewhere again.

[00:38:12]Let's do it.

[00:38:20]6 into 3.14 into 8 6 into 3.14 into.8 and hate.

[00:38:29]Yes.

[00:38:44]One sec.

[00:38:47]15.072 15.072 into 10^ minus 3. Correct? Yes. 15 into 10^ minus 3. Correct? Yes. Yes. Yes. 15.

[00:39:00]Yes. Option A. Yes. Correct. Correct.

[00:39:03]Nice.

[00:39:05]The question.

[00:39:08]Huh. The amount of energy required to form a soap bubble of radius 2 cm uh from a soap solution is nearly.

[00:39:19]gain surface tension concept there was no surface energy. So now I am creating that surface.

[00:39:52]So what are we doing? Soap bubble. Soap bubble we have air fluid.

[00:40:11]So two surfaces.

[00:40:13]So surface tension formula is energy per unit area. So T into A is equal to energy. It is the energy required to form a soap bubble. Surface tension 0.03 into area of 2 * spare sphere surface area. So 2 into 4 into<unk> into r².

[00:40:37]So 2 by 100 by 100 radius is 2 cm. So the meter 2 by 100 the whole square. So solve poloma 0.03 into 2 into 4 into<unk> into 4 into 10^ -4. Okay sol again multiplication.

[00:41:04]Good boys you do the math. Multiply what will we get? 0.03 0.03 03 into 2 into 4 into<unk> into 4 2 into 4 into 3.14 into 4 3.

[00:41:29]Yes.

[00:41:34]Okay.

[00:41:36]3 point right. So 3 into 10^ -4 yes option B correct answer 95% okay good man good 95% so good job keep it Vis and Viveum. Nice to meet you.

[00:42:16]Right.

[00:42:17]Continue.

[00:42:20]Let's go to the next question.

[00:42:27]Vary meter works on me engineering college. Okay. This is neat.

[00:42:40]So this is flat and this is me. So it works based on principle obviously principle energy conservation pressure.

[00:42:59]So potential changeinetic and pressure intercon. So you have low velocity, high pressure, high velocity, low pressure. So it'll get interchanged.

[00:43:09]So works on Bernal's principle.

[00:43:14]Option A correct.

[00:43:16]The question, two copper vessels A and B have the same base area but of different shapes.

[00:43:27]A takes twice the volume of water as that of B cherry. Same base area in a cricket have the same base area. All right. But different shapes. So simple, easy to calculate.

[00:43:57]A takes twice the volume of water as of B. So volume base area same height. Okay height same they have the same height.

[00:44:22]Question the correct statement among the following is vessel B weighs twice that of A. Again exact twice pressure on the base of the same pressure on the base area of SL A and B are same exactly. So pressure depends on height alone. So height is same. So fluid pressure depends only on height. So pressure hydrostatic paradox if you remember hydrostatic paradox right let's say so straight obviously we'll have the same pressure I'll have the same pressure hydrostatic pressure hydrostatic principle paradox hydrostatic paradox logic same height same pressure nothing Add it. The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm/s. All right. If the viscosity of the oil at room temperature is 0.9 kg per meter per second, the viscous drag forces. So Stokes formula Yeah. Stokes formula Stokes 6 pi r into e v. So dire they have asked us to calculate the drag force 6 into 22 by 7 r 5 mm. So 5 into 10^ -3 into ea 0.9 into v velocity 10 cm/ second. So 10 into 10^ - 2.

[00:46:56]Okay. 22 by 7 we'll take it as 3.14.

[00:47:03]Let's do the math.

[00:47:11]So numbers 6 into 3.14 6 into 3.14 into 5 into.9 5 into.9.

[00:47:26]So 84.7.

[00:47:31]So in the numbers multiply number I get 84.7 into 10 ^ So I'll have -1 10^ -4.

[00:47:45]So what are my options? 10^ -5 10 by 10 847 option. So if you want 8.47 47 8.47 into 10^ -5 right so 8.47 into 10^ sorry sorry minus 3 I forgot basic math 10 by 10 + 10 yes correct so 8.47 into 10^ minus 3 8.47 47 into 10^ minus 3 correct answer.

[00:48:26]Yes. Answer option B question just basic formula mechanics.

[00:48:44]Let's do this. A spherical ball is dropped in a long column of highly viscous liquid. The curve in the graph shown which represents the speed of the ball as a function of time multiple places u= 0 initial velocity 0.

[00:49:10]So it should start from zero.

[00:49:14]It should start from zero C and D right. Second viscous liquid, highly viscous liquid in the speed zero speed but gain viscous force depends on velocity velocity.

[00:49:46]So he'll reach terminal velocity. So velocity it keeps increasing up to particular value.

[00:50:02]So obviously option B it keeps increasing not possible increase.

[00:50:09]So it is just option B.

[00:50:13]Okay. Yes. Option B.

[00:50:17]H.

[00:50:19]Next question.

[00:50:23]If a soap bubble expands, the pressure inside the bubble is so inside pressure formula P outside plus 2T by R mostly constant 2T by Ren expand. If it expands value which means in the term overall value will go down decrease. So pressure inside will be decreasing.

[00:50:58]So bubble expand pressure decreases.

[00:51:13]Right.

[00:51:16]It's going to be harder.

[00:51:31]All right.

[00:51:38]It would be easy for you.

[00:51:41]Next question.

[00:51:44]The velocity of a small ball of mass m and density d when dropped in a container filled with the glycerin becomes constant after some time. The density of the glycerin is dx2. Then the viscous force acting on the ball is. So first free body diagram.

[00:52:21]Force buoyant viscous force. Boyce formula density of the liquid.

[00:52:29]Density of the liquid density.

[00:52:32]Density of the liquid is d by 2 into volume into g.

[00:52:40]Right. So d into volume into g viscous force formula six okay then the viscous force acting on him socions I think basic just going to startics.

[00:53:21]So free body diagram viscous force plus buoyant force is equal to weight of viscous force is equal to d vg weight minus d by 2 vg which is d by 2 vg dvn that is mass is equal to density into volume mg by 2. So viscous force is just mg by 2 stokes.

[00:54:08]Okay, let's let's write the Stokes law formula. 6 pi r into ecosity velocity.

[00:54:21]So we cannot use this formula.

[00:54:42]velocity constant. No force, no acceleration, terminal velocity.

[00:54:48]All right.

[00:54:52]A capillary tube of radius R is immersed in a water and water raises in it to a height h. Okay. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2 R is immersed in water.

[00:55:08]The mass of the water will raise in this tube is again just direct.

[00:55:25]So capillary rays in 2t cos theta by row rg correct by row rg. So surface tension r is equal to 2t cos theta by row rg one secondar radius height then water in the capillary is 5 g mass radius height mass So in the row into r into how row r is equal to 2t the gt surface tension that is constant. G acceleration due to gravity constant.

[00:56:29]Theta angle of contact for the given materials constant change from here. What can you say? Row one R1 H1 equals constantity mass by volume.

[00:56:54]So density m_sub_1 by v_sub_1 r1 h1 equals constant. Again capillary tube volume r² hap tube cylinder. So m1 by<unk> r1² h into r1 h1 equals constant.

[00:57:21]So h1 h1 cancel r r r r r r r r r r r r r r r r r r r r r cancel. So m1 by r1 equals constant.

[00:57:32]So m1 by m_sub_2 equals or m1 by r1= m_sub_2 by r2.

[00:57:42]If the capillary tube of radius 2 r 2 r m1 by r equals m_sub_2 by 2 r so cancel m_sub_1 into 2 = m_sub_2.

[00:58:02]So m1 value 5 g. So 5 into 2 10 g equals m_sub_2.

[00:58:12]All good guess we'll get the solution.

[00:58:25]Okay children.

[00:58:29]Okay.

[00:58:31]Right. So I hope questions I mean limited questions you try to do more questions 2020.

[00:58:41]Yeah four years and go through all the formulas formulas.

[00:58:51]So, formulas, speed of practice, practice. I'll see you in the next session with another new chapter. All the best. Take care. Bye-bye.