Advertisements
Advertisements
Question
Estimate the speed of vertically falling raindrops from the following data. Radius of the drops = 0.02 cm, viscosity of air = 1.8 × 10−4 poise, g= 9.9 × 10 ms−2 and density of water = 1000 kg m−3.
Advertisements
Solution
Given:
Radius of the drops r = 0.02 cm = 2 × 10−4 m
Viscosity of air η = 1.8 × 10−4 poise = 1.8 × 10−5 decapoise
Acceleration due to gravity g = 9.9 m/s2
Density of water ρ = 1000 kg/m3
Let v be the terminal velocity of a drop.
The forces acting on the drops are
(i) The weight mg acting downwards
(ii) The force of buoyance, i.e., \[\left( \frac{4}{3} \right) \pi r^3 \rho g\] acting upwards
(iii) The force of viscosity, i.e., 6πηrv acting upwards
Because the density of air is very small, the force of buoyance can be neglected.
From the free body diagram:
\[6\pi\eta \text{ rv = mg }\]
\[6\pi\eta rv = \frac{4}{3}\pi r^3 \rho g\]
\[v = 2 r^2 \frac{\rho g}{9\eta}\]
\[= 2 \times \left( 0 . 02 \times {10}^{- 2} \right)^2 \times 1000 \times \frac{\left( 9 . 9 \right)}{9} \times \left( 1 . 8 \times {10}^{- 5} \right)\]
\[ = 5 \text{ m/s }.\]
Hence, the required vertical speed of the falling raindrops is 5 m/s.
APPEARS IN
RELATED QUESTIONS
Fill in the blanks using the word(s) from the list appended with each statement
Viscosity of gases. .. with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
Explain why The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
(a) What is the largest average velocity of blood flow in an artery of radius 2 × 10–3 m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10–3 Pa s).
The force of viscosity is
The viscous force acting between two layers of a liquid is given by \[\frac{F}{A} = - \eta\frac{dv}{dz}\]. This F/A may be called
A raindrop falls near the surface of the earth with almost uniform velocity because
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)
Derive the expression for the terminal velocity of a sphere moving in a high viscous fluid using stokes force.
Derive Poiseuille’s formula for the volume of a liquid flowing per second through a pipe under streamlined flow.
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.
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 ______.
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is `"d"/2`, then the viscous force acting on the ball will be ______
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is `"d"/2` , then the viscous force acting on the ball will be ______.
Is viscosity a vector?
An air bubble of negligible weight having radius r rises steadily through a solution of density σ at speed v. The coefficient of viscosity of the solution is given by ______.
A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of density ρ2 (ρ2 < ρ1). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., `"F"_"viscous"`= -kv2 (k > 0). The terminal speed of the ball is ______.
