Mechanical education hub

Vapour pressure (P v ) Let us consider a closed container that is partially filled with liquid. Now what happened is evaporation takes place inside the container. The air above the liquid can absorb the water vapour molecules upto a certain limit and this limit is known as saturation limit. As we saw in surface tension of  Lecture - 5  that the molecules present inside the water are under balanced Cohesive forces so they are stable and molecules present on the surface of water are under unbalanced Cohesive forces so they are under unstable conditions. Therefore the molecules on surface of liquid are in highly excited state and by taking energy from molecules below it these molecules will evaporate. The air above the liquid will absorb these molecules only upto saturation. A saturation is such a condition in which the number of molecules evaporating from surface will become equal to the number of molecules rejoining the surface on condensation and such a situation is kn...

Before moving to this lecture I advise you guys to clear your concepts of capillarity which is mention in  Lecture - 5 . You also need to clear your concepts of Cohesion and adhesion which is mention in  Lecture - 1 . Capillarity rise 'h'   In the figure shown below a beaker is there which is filled with water and a test tube is dip inside it. Now what going to happen is that we will see Rise of water level inside test tube and it is known as capillarity rise. This rise of water level is denoted by 'h'. The main reason behind this rise water in test tube is adhesion, as we know adhesion is the intermolecular force of attraction between molecules of different nature and here water in contact with glass show adhesion more. But this rise in test tube is up to a certain limit because it is resisted by Gravity. Here to weight of fluid which is acting downward will resist the capillary rise. Here concave meniscus is formed because of adhesion. The reason is that...

Hey guys before going through this lecture, first of all you should clear your concepts of surface tension. That's why I recommend you to go through  Lecture - 5  first. Pressure inside a liquid droplet   Here, we will calculate gauge pressure (P gauge ). Gauge pressure is the pressure measured by considering that the atmospheric pressure is zero. We will have a detailed discussion on all types of pressure in my upcoming lectures. Let me clear one thing that there is a difference between a water droplet and bubble. Water droplet is filled with water from inside and outside atmosphere is present whereas in bubble inside the liquid film also air is present and of course outside of liquid film of bubble air is present. Remember we are considering atmospheric pressure is zero. On The Water droplet two forces are acting one is constructive force and other is destructive force. Water droplet is formed with the equilibrium of both these forces. Pressure from inside of water...

Shear force required for linear velocity profile   Let us consider a thin plate moving over the fluid surface with velocity 'V'. The distance between the bottom of the fluid and surface of fluid is represented by 'y' and this distance is very small. In the below diagram the deformation of fluid particles is shown which is due to the force represented as 'F'. Now take two layers of fluid into consideration and distance between these two layers is represented by 'dy'. 'θ' represents the angle of deformation of fluid particles. In the figure notice that triangle ABC is formed between the plate and bottom of the fluid and triangle A'B'C' is formed between two layers of fluids. Distance AC is represented by 'Vt' because Distance (AC) = velocity (V) * time (t) Similarly distance A'C' is represented by 'dut'. 'du' is the differential speed.  In ΔABC   Tan θ = Vt/y  In ΔA'B'C'   ...

Newtonian fluids   All those Fluids are known as newtonian Fluids for which shear stress (τ) is directly proportional to rate of shear strain (dθ/dt).  τ ∝ dθ/dt  τ = μ*(dθ/dt) or τ = μ*(du/dy)  ; because from derivation in  Lecture - 4  we know that dθ/dt = du/dy Above equation is also termed as newton's law of viscosity. The relation of above equation is linear, where μ represent viscosity and is constant with respect to rate of shear strain.  in the below figure graphical representation of different Newtonian fluids are shown-  In above graph oil is having maximum slope because viscosity in oil is more and air is having minimum slope because viscosity of air is less, whereas water lies between oil and air because viscosity of water is less than oil but more than air. A straight line passing through origin having constant slope is representing Newtonian fluids. Example are water, oil, mercury, air, petrol. Non Newtonian fl...

Surface tension (σ)   Let us consider a molecule 'A' which is under the surface of water. This molecule is completely surrounded by Cohesive forces of another molecules of water. Therefore this molecule is under the action of Balanced cohesive forces and hence it is in equilibrium.  Let us consider another molecule 'B' which is on the surface of the water, hence it is not completely surrounded by Cohesive forces. Therefore this molecule is under the action of unbalanced Cohesive forces and hence this molecule experiences a pull or stretch.  Due to above reason the molecules on surface experiences a pull and it appears that there is some kind of membrane over the surface of fluid. This membrane is having the ability to bear small loads and this phenomenon is known as surface tension. The main reason of surface tension is unbalanced Cohesive forces. With increase in temperature surface tension decreases due to breaking of Cohesive forces. One more thing to obs...

Viscosity   Viscosity represents the internal resistance offered by one layer of fluid to the adjacent layer. S.I unit of viscosity is kilogram per metre second. Basically it is fluid friction. More the viscosity means more fluid friction and vice versa. This is also called dynamic viscosity and absolute viscosity. This is absolute quantity because it is a direct measurement of internal resistance between the layers of fluids. We can differentiate between fluids just by observing that which fluid has more viscosity and which one has less viscosity. In case of liquids the main reason of viscosity is intermolecular bonding (cohesion). Whereas in case of gases the main reason of viscosity is molecular collision. In below figure fluid is there which moves from its initial position due to the action of shear force. We consider a very small elemental thickness of fluid and study it separately. Let us consider this elemental thickness to be so small that it includes only ...

Compressibility (β)   Compressibility is defined as the variation of volume(V) or densityWith respect to pressure with constant mass (m). If variation of volume with respect to pressure is high then compressibility is high. Liquids are generally incompressible whereas gases are generally highly compressible. Two Piston cylinder arrangement is shown in below figure one arrangement is filled with liquid and other arrangement is filled with gas. In case of liquid with increase in pressure, the volume and density remains unchange. In case of gas as we increase the pressure, volume start decreasing and density start increasing. Therefore liquid is incompressible and gas is compressible. Experimentally it was found that air is 20000 times more compressible then Water. An experiment was conducted to check the compressibility of water. In that experiment the density of water at 1atm pressure was 998 kilogram per metre cube, after that when the pressure was increased ...

Properties are certain measurable characteristics that can be quantified. with the help of properties we can easily identify the fluids. Properties of fluids are as follows- Density or mass density (ρ)   Density is defined as the ratio of mass per unit volume. The international System of units ( SI units ) is Kilogram per metre cube (kg/m^3). Density basically represent the number of molecules in a given volume of fluid. As we increase the number of molecules in a given volume its mass will increase and fluid become heavy.                 Density (ρ) = mass/volume                                     ρ = m/V Density of water = 1000 kg/m^3 Density of Mercury = 13600 kg/m^3 Density of air = 1.2 kg/m^3 Density of petrol = 750 kg/m^3 Density of diesel = 850 kg/m^3 Density of solids is always greater than density of liquids and d...

Fluids The fluid is a substance that is having the ability to flow or deform continuously under the action of shear force, no matter how much small the force is. All types of liquids and gases are known as fluids. Examples are water, Mercury, steam, air. If fluid is static or stationary then it means no shear force acting on it. In the above diagram initially when fluid is static we consider some molecules of fluids which are in straight line. After that when shear force is applied, for the time interval 't1' those molecules change their position with angle ' θ1'  except one molecule which is at boundary because we are considering no slip condition. In upcoming lectures we study about no slip conditions. Similarly after time interval 't2' molecules change it's position by 'θ2'. 'P atm  ' is the atmospheric pressure acting on surface of fluid. Difference between solids and fluids In case of solids the deformation is...

Mechanical advantage   It is defined as the ratio of the force produced by a machine to the force applied to it, used in assessing the performance of machine.  The combination of pulley system is shown in the below figure-  Here for lifting download F force is required but the effort given to the system is 8 times less, which is the good example of mechanical advantage. For the above system mechanical advantage is 8 Mechanical advantage = load / effort  Mechanical advantage for linear motion is -  Mechanical advantage for angular motion is -  Efficiency of system or mechanism Efficiency of the system is defined as the ratio of output power to the input power. PROBLEM - Find out mechanical advantage of the given mechanism having 100% efficiency. Solution -  In the sense of angular velocity It means that above mechanism is toogle mechanism.  Toggle mechanism   Those mechanism whose mechan...

DOUBLE SLIDER CRANK MECHANISM   Double slider crank mechanism is a combination of four links having two turning pairs and two sliding pairs. Diagram of this mechanism is shown below- This mechanism consists of three inversions as listed below- First inversion (fixed slotted plate) Second inversion (fixed slider) Third inversion (fixed connecting rod) First inversion    When slotted plate is fixed then it become the first inversion of double slider crank mechanism. Its example is elliptical trammel. Diagram of elliptical trammel is shown below-  An electrical trammel is a simple mechanism which can trace exact elliptical path. It consists of two shuttles which are are confined to perpendicular channels or Rails, and a rod which is attached to shuttles by pivots at fixed position along the rod. As shuttle moves back and forth, each along its channel, the end of the rod moves in an elliptical path. Elliptical trammel is used in aut...