Question:
Raindrops are falling from a certain height. Assume all raindrops are spherical and have same drag coefficient. The impact speed of large raindrops compared to that of small raindrops is
Raindrops are falling from a certain height. Assume all raindrops are spherical and have same drag coefficient. The impact speed of large raindrops compared to that of small raindrops is
Updated On: Jan 18, 2023
- greater
- smaller
- same
- depends on height
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The Correct Option is A
Solution and Explanation
When the raindrops attains terminal velocity the net force acting on the body is zero.
$\therefore W-T-F=0$ or $F=W-T$
$ \Rightarrow 6 \pi \eta r v=\frac{4}{3} \pi r^{3} \rho g-\frac{4}{3} \pi r^{3} \sigma g$
$=\frac{4}{3} \pi r^{3}(\rho-\sigma) g$
$ \therefore$ Terminal velocity $v=\frac{2}{9} \frac{r^{2}(\rho-\sigma) g}{\eta}$ or $v \propto r^{2}$
Hence, the impact speed of large raindrops is greater as compared to the small raindrops.
$\therefore W-T-F=0$ or $F=W-T$
$ \Rightarrow 6 \pi \eta r v=\frac{4}{3} \pi r^{3} \rho g-\frac{4}{3} \pi r^{3} \sigma g$
$=\frac{4}{3} \pi r^{3}(\rho-\sigma) g$
$ \therefore$ Terminal velocity $v=\frac{2}{9} \frac{r^{2}(\rho-\sigma) g}{\eta}$ or $v \propto r^{2}$
Hence, the impact speed of large raindrops is greater as compared to the small raindrops.
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Concepts Used:
Viscosity
Viscosity is a measure of a fluid’s resistance to flow. The SI unit of viscosity is poiseiulle (PI). Its other units are newton-second per square metre (N s m-2) or pascal-second (Pa s.) The dimensional formula of viscosity is [ML-1T-1].
Viscosity: Formula
Viscosity is measured in terms of a ratio of shearing stress to the velocity gradient in a fluid. If a sphere is dropped into a fluid, the viscosity can be determined using the following formula:
η = [2ga2(Δρ)] / 9v
Where ∆ρ is the density difference between fluid and sphere tested, a is the radius of the sphere, g is the acceleration due to gravity and v is the velocity of the sphere.
Viscosity: Types
- Dynamic viscosity: When the viscosity is measured directly by measuring force. It is defined as the ratio of shear stress to the shear strain of the motion. Dynamic viscosity is used to calculate the rate of flow in liquid.
- Kinematic viscosity: There is no force involved. It can be referred to as the ratio between the dynamic viscosity and density of the fluid. It can be computed by dividing the dynamic viscosity of the fluid with fluid mass density.
- Laminar flow: Laminar flow is the type of flow in which the fluid moves smoothly or in a regular path from one layer to the next. Laminar flow occurs in lower velocities.