a rain drop of radius 0.3mm has a terminal velocity in air 1m/s. the viscosity of air is 18×10^-5 dyne cm^-2 s. find the viscous force on the rain drops in newton.
F=6pie.n.r.v
=6*(3.14)*18*10^-5*0.3*10^-3*1
=1017.3*10^-4N
To find the viscous force on the raindrop, we can use Stokes' law, which relates the viscous force to the size and velocity of the droplet.
Stokes' law formula:
F = 6πηrv
Where:
F = Viscous force
η = Viscosity of the fluid (air in this case)
r = Radius of the droplet
v = Terminal velocity of the droplet
Given:
r = 0.3 mm = 0.3 × 10^-2 cm
v = 1 m/s
η = 18 × 10^-5 dyne cm^-2 s
First, we need to convert the radius from cm to meters:
r = 0.3 × 10^-2 cm = 0.3 × 10^-4 m
Now, we can substitute the values into the formula and solve for the viscous force (F):
F = 6π × (18 × 10^-5) × (0.3 × 10^-4) × (1)
F = 3.816 × 10^-7 N
Therefore, the viscous force on the raindrop is approximately 3.816 × 10^-7 Newtons.
To find the viscous force on the raindrop, we can use Stoke's Law, which relates the viscous force on an object moving through a fluid to its velocity and the dynamic viscosity of the fluid.
Stoke's Law states that the viscous force (F) acting on a spherical object moving through a fluid is given by:
F = 6πηrv
where:
F is the viscous force,
η is the dynamic viscosity of the fluid,
r is the radius of the raindrop, and
v is the velocity of the raindrop.
Given:
Radius of the raindrop, r = 0.3 mm = 0.03 cm
Terminal velocity of the raindrop, v = 1 m/s
Viscosity of air, η = 18 × 10^-5 dyne cm^-2 s
First, we need to convert the given radius from mm to cm:
r = 0.3 mm = 0.3/10 cm = 0.03 cm
Now, we can substitute the given values into the Stoke's Law equation to calculate the viscous force:
F = 6πηrv
= 6π(18 × 10^-5 dyne cm^-2 s)(0.03 cm)(1 m/s)
= 6π(18 × 10^-5 N m^-2 s)(0.03 cm)(1 m/s) [Note: 1 dyne cm^-2 = 1 N m^-2]
= 6π(18 × 10^-5 N m^-2 s)(0.03 × 10^-2 m)(1 m/s) [1 cm = 10^-2 m]
= 6π(18 × 10^-5 N m^-2 s)(0.3 × 10^-3 m/s)
= (6π × 18 × 10^-5 × 0.3 × 10^-3) N
= (3.24 × 10^-5) N
Therefore, the viscous force acting on the raindrop is approximately 3.24 × 10^-5 Newton (N).