Advertisements
Advertisements
प्रश्न
Derive the expression for the terminal velocity of a sphere moving in a high viscous fluid using stokes force.
Advertisements
उत्तर
Expression for terminal velocity: Consider a sphere of radius r which falls freely through a highly viscous liquid of coefficient of viscosity η. Let the density of the material of the sphere be ρ and the density of the fluid be σ.
Forces acting on the sphere when it falls in a viscous liquid
Gravitational force acting on the sphere,
FG = mg = `4/3π"r"^3ρ"g"` (downward force)
Upthrust, U = `4/3π"r"^3σ"g"` (upward force)
Viscous force, F = 6πηrvt
At terminal velocity vt,
Downward force = upward force
FG = U + F
FG − U = F ⇒ `4/3π"r"^3ρ"g" - 4/3π"r"^3σ"g"` = 6πηrvt
vt = `2/9 xx ("r"^2(ρ - σ))/η` g ⇒ `"v"_"t" ∝ "r"^2`
Here, it should be noted that the terminal speed of the sphere is directly proportional to the square of its radius. If a is greater than ρ, then the term (ρ – σ) becomes negative leading to a negative terminal velocity.
APPEARS IN
संबंधित प्रश्न
In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 × 10–5 m and density 1.2 × 103 kg m–3? Take the viscosity of air at the temperature of the experiment to be 1.8 × 10–5 Pa s. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.
The force of viscosity is
Water flows at a speed of 6 cm s−1 through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. Is it a steady flow?
The unit of viscosity is
In a horizontal pipe of non-uniform cross-section, water flows with a velocity of 1 ms−1 at a point where the diameter of the pipe is 20 cm. The velocity of water (1.5 ms−1) at a point where the diameter of the pipe is (in cm)
A block of Ag of mass x kg hanging from a string is immersed in a liquid of relative density 0.72. If the relative density of Ag is 10 and tension in the string is 37.12 N then compute the mass of Ag block.
Why two holes are made to empty an oil tin?
The tangential force or viscous drag on any layer of the liquid is directly proportional to the velocity gradient `"dv"/"dx"`. Then the direction of dx velocity gradient is ____________.
In motors, more viscous oil is used in summer than in winter due to ____________.
The velocity of water in river is 8 km/hr of the upper surface. The river is 12 m deep. If the coefficient of viscosity of water is 10-2 poise then the shearing stress between horizontal layers of water is ______.
