RBSE Class 11 Physics Notes Chapter 10 Mechanical Properties of Fluids

These comprehensive RBSE Class 11 Physics Notes Chapter 10 Mechanical Properties of Fluids will give a brief overview of all the concepts.

RBSE Class 11 Physics Chapter 10 Notes Mechanical Properties of Fluids

→ Pascal’s Law:
According to the Pascal’s law, pressure applied to an enclosed fluid is transmitted undiminshed to every point of the fluid and the walls of the container.

→ Coefficient of Viscosity:
It is defined as the tangential force required per unit area to maintain unit velocity gradient.

→ Viscous force, F = -η A\(\frac{d v}{d x}\)

→ Stoke’s Law:
The retarding force F due to viscous drag for a spherical body of radius r moving with a velocity v in a liquid with coefficient of viscosity T) is:
F = 6πη r v

→ Terminal velocity:
v = \(\frac{2}{9} \frac{r^2(\rho-\sigma)}{\eta}\) g

→ The velocity of flow is independent of the nature of the liquid. The velocity of flow will increase if the cross-section decreases and vice-versa.

 

→ Reynold established that in case of motion of fluids in thin tubes' critical velocity depends on:

• density (ρ)
• viscosity (η) of the fluid, and
• radius of the tube (r).v_c = R\(\left(\frac{\eta}{\rho D}\right)\)
  where R is Reynold’s number.
  R ≤ 2000, for steady flow.

→ Equation of Continuity
A₁v₁ = A₂v₂

→ Bernoulli’s Theorem:
It states that the sum of the energies possessed by a flowing ideal liquid at any point is constant, given that the liquid is non-viscous and incompressible and its flow is stream-line, i.e.,
P + \(\frac{1}{2}\)ρv² + ρgh = constant.

→ Bernoulli’s theorem for horizontal motion,
P₁ + \(\frac{1}{2}\)ρv₁² = P₂ + \(\frac{1}{2}\)ρv₂²

→ The volume flowing past a cross-section through a venturimeter,
ΔV = A₁A₂\(\sqrt{\frac{2 g h}{\left(A_1^2-A_2^2\right)}}\)

→ Surface tension is the property of the liquid due to which its free surface tries to have minimum surface area.

→ The unit of surface tension is N/m and its dimensional formula is [M¹L⁰T^-2].

→ Adhesive forces are the forces of attraction between the molecules of different substances.

→ Cohesive forces are the forces of attraction between the molecules of same substances.

→ Surface tension depends only on the nature of the liquid. It is independent of the surface area.

→ Work done in forming a drop or bubble in liquid,
W = T(πr²)

→ Work done for a bubble in air,
W = 2T(4πr²)

→ Pressure P = \(\frac{F}{A}\)

→ Pressure of liquid P = ρgh

→ Pascal s law : P₁ = P₂ or \(\frac{F_1}{A_1}=\frac{F_2}{A_2}\)

→ Velocity gradient = \(\frac{\Delta v}{\Delta x}\)

→ Viscous force F = -ηA\(\frac{\Delta v}{\Delta z}\)

→ Stoke’s law : F = 6πηrv

→ Terminal velocity v_t = \(\frac{2 r^2(\rho-\sigma) g}{9 \eta}\)

→ Reynold’s number R = \(\frac{\rho v_c D}{\eta}\)

→ Equation of continuity: A₁v₁ = A₂v₂

→ Pressure energy of unit volume : E_pr = \(\frac{P}{\rho}\)

→ Bernoulli’s Theorem : P + \(\frac{1}{2}\)ρv² + ρgh = constant
For horizontal flow P + \(\frac{1}{2}\)ρv²= constant

→ Rate of flow of liquid through venturimeter
Q = A₁A₂\(\sqrt{\frac{2 g h}{\left(A_1^2-A_2^2\right)}}\)

→ Velocity of efflux v = \(\sqrt{2 g h}\)

→ Surface tension T = or T = \(\frac{\Delta W}{\Delta A}\)

→ Surface energy E_s = W = TΔA

→ Excess pressure inside drop P_drop = \(\frac{2 T}{R}\)

→ Excess pressure in bubble P_pressure = \(\frac{4 T}{R}\)

→ Elevation in capillary h = \(\frac{2 T \cos \theta}{r \rho g}\)

→ Surface tension (from capillary rise) T = \(\frac{r h \rho g}{2 \cos \theta}\)

→ Specific gravity:
The relative density or specific gravity of a substance is defined as the ratio of the density of the substande to the density of water at 4°C.

→ Buoyancy:
The upward force acting on a body immersed in a fluid is called upthrust.

→ Laminar flow:
The steady flow in which liquid moves in the form of layers is called laminar flow. The velocity of the layer varies from maximum at axis to zero for the layer at the wall of the tube.

→ Ideal fluid:
An ideal fluid is one which is non-viscous, incompressible, and its flow is steady and irrotational.

→ Magnus effect:
The difference in lateral pressure, which causes a spinning ball to take a curved path which is convex towards the greater pressure side, is called magnus effect.

→ Sphere of influence:
It is a sphere drawn with the molecule as a centre and molecule range as radius.

→ Capillarity:
A tube of very fine bore is called a capillary tube. The phenomenon of rise or fall of a liquid in capillary tube is known as capillarity.