The velocity of water in a river is $18\, km/hr$ near the surface. If the river is $5\, m$ deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water $= 10^{-2}$ poise.
- $10^{-1} N/m^2$
- $10^{-2} N/m^2$
- $10^{-3} N/m^2$
- $10^{-4} N/m^2$
The Correct Option is C
Solution and Explanation
Top Questions on Viscosity
In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the following circuit. He applied a resistance of \( 520 \, \Omega \) in \( R \). When \( K_1 \) is closed and \( K_2 \) is open, the deflection observed in the galvanometer is 20 div. When \( K_1 \) is also closed and a resistance of \( 90 \, \Omega \) is removed in \( S \), the deflection becomes 13 div. The resistance of galvanometer is nearly:
- KCET - 2025
- Physics
- Viscosity
- The diameter of spherical galena particles that have the same settling velocity as spherical quartz particles of diameter 25 μm (both settling in water) is ............. μm (rounded off to one decimal place). Assume Stokes law of settling to be valid. Given: Density of galena = 7400 kg m$^{-3}$, density of quartz = 2600 kg m$^{-3}$, density of water = 1000 kg m$^{-3}$.
- For an application where the Reynolds number is to be kept constant, a liquid with density of 1 g per cubic cm and viscosity of 0.01 Poise results in a characteristic speed of 1 cm per second. If this liquid is replaced by another with density of 1.25 g per cubic cm and viscosity of 0.015 Poise, the characteristic velocity will be ........... cm per second (rounded off to one decimal place). Assume the characteristic length of the flow to be the same in both cases.
- Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities? Given: Delta P is the difference between the outlet and inlet pressure, mu is the dynamic viscosity of the liquid, and R and L are radius and length of the pipe, respectively.
- At high temperatures, which one of the following empirical expressions correctly describes the variation of dynamic viscosity \(\mu\) of a Newtonian liquid with absolute temperature \(T\)? (Given: \(A\) and \(B\) are positive constants.)
Questions Asked in JEE Main exam
The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.
- JEE Main - 2025
- Kinematics
The least acidic compound, among the following is
- JEE Main - 2025
- Organic Chemistry
Choose the correct set of reagents for the following conversion:
- JEE Main - 2025
- Organic Chemistry
- JEE Main - 2025
- Organic Chemistry
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Permutations
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.