Revision: Class 11 >> Mechanical Properties of Fluids: Viscosity NEET (UG) Mechanical Properties of Fluids: Viscosity

The force which produces compression is called thrust. Its S.I unit is the newton.

High pressure is an area of the atmosphere where the barometric pressure is higher than its surrounding areas. In this case, the wind from the center of high pressure blows towards the surrounding low-pressure areas.

A low-pressure area is an area in the atmosphere where the pressure is lower than its surrounding areas. In this situation, the wind from the surroundings blows towards the center of low pressure.

The pressure exerted by this mercury column is considered as the pressure of magnitude ‘one atmosphere’ (1 atm).

SI unit of pressure is the pascal (Pa) or Nm⁻²
One Pascal: When a force of one newton acts normally on an area of one square metre (1 m²) then the pressure acting on the surface acting on the surface is called one Pascal.

RELATIVE DENSITY: “is the ratio of the density of a substance to the density of water at 4° C.”
Or
RELATIVE DENSITY “is the ratio of the mass of the substance to the mass of an equal volume of water at 4° C.”

Density of a substance is defined as “Mass per Unit volume”.

Density [d]=`"mass  of the substance"/"volume of the substance"`

d=`m/v`

UNIT OF RELATIVE DENSITY: No units since it is a pure ratio.

The coefficient of viscosity of a liquid is defined as the viscous force acting tangentially per unit area of a liquid layer having a unit velocity gradient in a direction perpendicular to the direction of flow of the liquid.

The maximum constant velocity acquired by a body while falling freely through a viscous medium is called the terminal velocity V_T.

The rate of change of velocity (dv) with distance (dx) measured from a stationary layer is called velocity gradient.

∴ Velocity gradient = `(dv)/dx`

(b) There is no gravitational force acting downwards. However, when the starting velocity is 20 m/s, the viscous force, which is directly proportional to velocity, becomes maximum and tends to accelerate the ball upwards.

\[\text{ When the ball falls under gravity, }\]

\[\text{ neglecting the density of air: } \]

\[\text{ Mass of the sphere = m }\]

\[\text{ Radius = r }\]

\[\text{ Viscous drag coeff . }= \eta\]

\[\text{Terminal velocity is given by}: \]

\[\text{ mg  }= 6\pi\eta r v_T \]

\[ \Rightarrow \frac{6\pi\eta r v_T}{m} = g . . . (1)\]

\[\text{ Now, at terminal velocity, the acceleration of the ball due to the viscous force is given by: } \]

\[a = \frac{6\pi\eta r v_T}{m}\]

\[\text{ Comparing equations (1) and (2), we find that : } \]

\[ \text{ a = g }\]

Thus, we see that the initial acceleration of the ball will be 9.8 ms - 2  .

(c) The velocity of the ball will decrease with time because of the upward viscous drag. As the force of viscosity is directly proportional to the velocity of the ball, the acceleration due to the viscous force will also decrease.

(d) When all the kinetic energy of the ball is radiated as heat due to the viscous force, the ball comes to rest.