Coefficient of Viscosity

Q.

What is the significance of the Reynolds number?

Q. The velocity distribution for the flow over a flat plate is given by $u=2y-y^2$ in which $u$ is the velocity in $\text{m/s}$ at a distance $y\text{metres}$ above the plate. Determine the shear stress at $y=0.15\text{m}$. Take dynamic viscosity of the fluid as $8.5\text{poise}$.

1. $1.455{\text{N/m}}^2$
2. $1.445{\text{N/m}}^2$
3. $1.554{\text{N/m}}^2$
4. $1.545{\text{N/m}}^2$

Q. Which of the following statements correctly gives the variation in the viscosities of a liquid and a gas with change in temperature?

1. Viscosity increases with increase in temperature for a liquid and decreases with increase in temperature for a gas
2. Viscosity increases with increase in temperature for a liquid and increases with increase in temperature for a gas
3. Viscosity decreases with increase in temperature for a liquid and decreases with increase in temperature for a gas
4. Viscosity decreases with increase in temperature for a liquid and increases with increase in temperature for a gas.

Q. A cubical block of side ${}^{\prime }{a}^{\prime }$ and density ${}^{\prime }{\rho }^{\prime }$ slides over a fixed inclined plane with constant velocity ${}^{\prime }{v}^{\prime }$ . There is a thin film of viscous fluid of thickness ${}^{\prime }{t}^{\prime }$ between the plane and the block. Then, the coefficient of viscosity of the thin film will be:
(Acceleration due to gravity is $g$)

1. $\frac{\rho {agt}^2\text{sin}\theta }{v}$
2. $\frac{\rho ag\sin \theta t}{v}$
3. $\frac{v}{\rho agt\sin \theta }$
4. None of these

Q. There is a $1\text{mm}$ thick layer of glycerine between a flat plate of area $100{\text{cm}}^2$ & a big fixed plate. If the coefficient of viscosity of glycerine is $1.0\text{kg/m-s}$, then how much force is required to move the plate with a velocity of $7\text{cm/s}$?

1. $7\text{N}$
2. $0.7\text{N}$
3. None of the above
4. $0.007\text{N}$

Q. A boat of area $10{\text{m}}^2$ floating on the surface of a river is made to move horizontally with a speed of $2\text{m/s}$ by applying a tangential force. If the river is $1\text{m}$ deep and the water in contact with the bed is stationary, find the tangential force needed to keep the boat moving with same velocity. (Assume the viscosity of water as $0.01\text{poise}$).

1. $0.02\text{N}$
2. $0.03\text{N}$
3. $0.04\text{N}$
4. $0.05\text{N}$

Q. Water flows between two plates, of which the upper one is stationary and the lower one is moving with a velocity $V$. What will be the velocity of the fluid in contact with the upper plate?

1. $V$
2. $\frac{V}{2}$
3. $2V$
4. $0$

Q. The velocity of water in a river is $18{\text{kmh}}^{-1}$ near the surface. If the river is $5\text{m}$ deep, then the shearing stress between the surface layer and the bottom layer is:
(Given - coefficient of viscosity of water, $\eta ={10}^{-3}\text{Pa.s}$)

1. ${10}^{-4}{\text{Nm}}^{-2}$
2. ${10}^{-5}{\text{Nm}}^{-2}$
3. ${10}^{-2}{\text{Nm}}^{-2}$
4. ${10}^{-3}{\text{Nm}}^{-2}$

Q. The shear stress at a point in a liquid is found to be $0.03{\text{N/m}}^2$. The velocity gradient for the fluid flow is $0.15{\text{s}}^{-1}$. What will be its viscosity (in $\text{Poise}$) ?

1. $2$
2. $0.2$
3. $0.5$
4. $20$

Q. We have three beakers containing glycerine, water and kerosene separately. They are stirred vigorously and placed on a table. The liquid which comes to rest at the earliest is

1. Glycerine
2. Water
3. Kerosene
4. All of them at the same time

Q. A Newtonian fluid fills the clearance between the shaft and the sleeve. When a force of $800\text{N}$ is applied to the shaft, parallel to the sleeve, the shaft attains a speed of $1.5\text{cm/sec}$. If a force of $2.4\text{kN}$ is applied instead, the shaft would move with a speed of

1. $1.5\text{cm/sec}$
2. $13.5\text{cm/sec}$
3. $4.5\text{cm/sec}$
4. None

Q. The space between two plates $20\text{cm}\times 20\text{cm}\times 1\text{cm},1\text{cm}$ apart is filled with a liquid of viscosity $1\text{Poise}$. The upper plate is dragged to the right with a force of $F=5\text{N}$ keeping the lower plate stationary. The upper plate is moving at a constant speed $u$ as shown in figure.


What will be the velocity in $\text{m/s}$ of the flow at a point $0.5\text{cm}$ below the lower surface of the upper plate if linear velocity profile is assumed for the flow ?

1. $1.25$
2. $2.5$
3. $0.25$
4. $6.25$

Q. Two horizontal plates placed $250\text{mm}$ apart have an oil layer of viscosity $20\text{poise}$ in between the plates. Calculate the shear stress on the oil layer, if the upper plate is moved with a velocity of $1250\text{mm/s}$.

1. $20{\text{N/m}}^2$
2. $2{\text{N/m}}^2$
3. $10{\text{N/m}}^2$
4. None of the above mentioned.

Q. A rectangular metal plate has dimensions of $10\text{cm}\times 20\text{cm}$. A thin film of oil separates the plate from a fixed horizontal surface. The separation between the lower surface of the rectangular plate and the upper portion of the horizontal surface is $0.2\text{mm}$. An ideal string is attached to the plate and passes over an ideal pulley to a mass $m$. When $m=125\text{gm}$, the metal plate moves at a constant speed of $5\text{cm/s}$ across the horizontal surface. Then, the coefficient of viscosity of oil in ${\text{dyne-s/cm}}^2$ is $(\text{Use}g=1000{\text{cm/s}}^2)$

1. $5$
2. $25$
3. $2.5$
4. $50$

Q. Which of the following graph shows the relation between shear stress and velocity gradient for a non-Newtonian fluid?

1. 
2. 
3. 
4. 

Q.

A sphere is dropped under gravity through a fluid of viscosity $h$. If the average acceleration is half of the initial acceleration, the time to attain the terminal velocity is $({\rho }_s=densityofthesphere,r=radius)$.

Q. A container filled with a viscous liquid is moving vertically downwards with a constant speed $3v_0$. At the instant shown, a sphere of radius $r$ is moving vertically downwards (in liquid) has speed $v_0$. There is no relative motion between fluid and container. The coefficient of viscosity is $\eta$. Then at the shown instant, the magnitude of viscous force acting on sphere is

1. $6\pi \eta r{v}_0$
2. $12\pi \eta r{v}_0$
3. $18\pi \eta r{v}_0$
4. $24\pi \eta r{v}_0$

Q. A plate of area $2{\text{m}}^2$ is made to move horizontally with a speed of $2\text{m/s}$ by applying a horizontal tangential force over the free surface of a liquid having depth of $1\text{m}$. If the coefficient of viscosity of liquid is $0.01\text{Poise}$, find the tangential force needed to move the plate.

1. $4\times {10}^{-3}\text{N}$
2. $3\times {10}^{-3}\text{N}$
3. $2\times {10}^{-3}\text{N}$
4. $1\times {10}^{-3}\text{N}$

Q. A square plate of $1\text{m}$ side moves parallel to a second plate with velocity $4\text{m/s}$. A thin layer of water exist between plates. If the viscous force is $2\text{N}$ and the coefficient of viscosity is $0.01\text{Poise}$, then find the distance between the plates.

1. $3\text{mm}$
2. $2\text{mm}$
3. $1\text{mm}$
4. $4\text{mm}$

Q. The ratio of radii of two wires of same material is $2:1$. If these are stretched by equal forces, find the ratio of stress produced in them.

1. 1 : 2
2. 2 : 1
3. 4 : 1
4. 1 : 4

Q. A cubical block (side $2\text{m}$) of mass $20\text{kg}$ slides on inclined plane lubricated with the oil of viscosity $\eta ={10}^{-1}\text{Poise}$ with constant velocity of $10\text{m/s}$. Find out the thickness of the layer of liquid. $(g=10{\text{m/s}}^2)$

1. $4\times {10}^{-3}\text{m}$
2. $3\times {10}^{-3}\text{m}$
3. $2\times {10}^{-3}\text{m}$
4. $1\times {10}^{-3}\text{m}$

Q. The velocity of water in a river is $18\text{km/hr}$ at the surface. If the river is $5\text{m}$ deep, find the shearing stress between the horizontal layers of water. The viscosity of water is ${10}^{-2}\text{Poise}$.

1. ${10}^{-3}{\text{N/m}}^2$
2. $2\times {10}^{-3}{\text{N/m}}^2$
3. $3\times {10}^{-3}{\text{N/m}}^2$
4. $4\times {10}^{-3}{\text{N/m}}^2$

Q.

Why do we treat air and vacuum similarly?Eg:The permittivity of air and vacuum is same

Q. The shear stress at a point in a liquid is found to be $0.03{\text{N/m}}^2$. The velocity gradient for the fluid flow is $0.15{\text{s}}^{-1}$. What will be its viscosity (in $\text{Poise}$) ?

1. $20$
2. $2$
3. $0.2$
4. $0.5$

Q. A man is rowing a boat with a constant velocity $v_o$ in a river of depth ${}^{\prime }{D}^{\prime }$. The contact area of boat is ${}^{\prime }{A}^{\prime }$ and coefficient of viscosity of water is $\eta$. Find the force required to row the boat.

1. $\frac{\eta v_o}{D}$
2. $\frac{\eta A^2{v}_o}{D}$
3. $\frac{\eta D^2{v}_o}{A}$
4. $\frac{\eta A{v}_o}{D}$

Q. The velocity distribution for the flow over a flat plate is given by $u=2y-y^2$ in which $u$ is the velocity in $\text{m/s}$ at a distance $y\text{metres}$ above the plate. Determine the shear stress at $y=0.15\text{m}$. Take dynamic viscosity of the fluid as $8.5\text{poise}$.

1. $1.455{\text{N/m}}^2$
2. $1.545{\text{N/m}}^2$
3. $1.445{\text{N/m}}^2$
4. $1.554{\text{N/m}}^2$

Q. A square plate of $0.1\text{m}$ side moves parallel to a second plate with a relative velocity of $0.1\text{m/s}$, both plates being immersed in water. If the viscous force is $0.002\text{N}$ and the coefficient of viscosity is $0.01\text{Poise}$, distance between the plates in $\text{m}$ is

1. $0.1$
2. $0.05$
3. $0.005$
4. $0.0005$

Q. There is a $1\text{mm}$ thick layer of glycerine between a flat plate of area $100{\text{cm}}^2$ & a big fixed plate. If the coefficient of viscosity of glycerine is $1.0\text{kg/m-s}$, then how much force is required to move the plate with a velocity of $7\text{cm/s}$?

1. $7\text{N}$
2. $0.7\text{N}$
3. $0.007\text{N}$
4. None of the above

Q. A ball is dropped in viscous liquid after some time it attains equilibrium, then

1. v = 0
2. v = horizontal
3. v = constant
4. v = variable

Q. The end of a capillary tube is immersed into a liquid. Liquid slowly rises in the tube up to some height. Then, the capillary - fluid system

1. Will absorb heat
2. Will release heat
3. Will not be involved in any heat transfer
4. Nothing can be said