# Viscosity

• Viscous force is the force of friction acting between two layers of fluids, opposing the relative motion of one over the other.
• When temperature increases viscosity of gases increases due to exchange of momentum.
• When temperature increases viscosity of liquids decreases due to decrease in cohesive forces.
• Velocity gradient is the ratio of difference in velocities and the distance between two points in the liquid.
• The viscosity and compressibility of an ideal fluid is zero.
• The viscous force acting between two adjacent layers of a liquid is directly proportional to the surface area of the layers in contact and the velocity gradient.
• Coefficient of viscosity is defined as the tangential force per unit area required to maintain unit velocity gradient.
• The ratio between the coefficient of viscosity and density of liquid is called coefficient of kinematic viscosity.
• If the flow is streamline velocity of liquid is proportional to pressure difference.
• When capillaries are connected in series volume of the liquid flowing per second is same.
• when capillaries are connected in parallel the total pressure remains constant.
• When the sum of viscous force and upthrust of the liquid on the body is equal to its weight.
• Terminal velocity is directly proportional to the square of the radius of the sphere.
• Terminal velocity and viscosity are inversely proportional to each other.
• When 'n' droplets are falling down with terminal velocity ν are combined and formed a big drop then terminal velocity of big drop Vbig = n2/3 Vsmall.

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1. The coefficient of viscosity for a fluid is defined as the ratio of shearing stress to the strain rate.
\eta=\frac{F/A}{v/l}=\frac{Fl}{vA}

2. Stoke's law: It is the viscous drag force F on a sphere of radius r moving with velocity v through a fluid of viscosity η.
F = 6 πηav

3. Terminal velocity: The maximum constant velocity acquired by the body while falling through a viscous fluid.

\tt v=\frac{2}{9}\times\frac{r^{2}\left(\rho-\sigma\right)g}{\eta}