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Question: The tangential forces per unit area of the liquid layer required to maintain unit velocity gradient ...

The tangential forces per unit area of the liquid layer required to maintain unit velocity gradient is known as:
A. Coefficient of gravitation of liquid layer
B. Coefficient of friction between layers
C. Coefficient of viscosity of the liquid
D. Temperature coefficient of viscosity

Explanation

Solution

When the surface is rough and an object is sliding on that surface some heat will be generated due to the interaction between the block and the surface. This is called friction between them and it is a contact force. Not only in this case and in case of liquids also there will be this hindrance force and we call it as a viscosity.

Formula used:
FV=−ηAdvdx{F_V} = - \eta A\dfrac{{dv}}{{dx}}

Complete step by step answer:
Normally fluids will be of two types. They are Newtonian fluids and non Newtonian fluids. The fluid which flows by obeying the newton laws are called Newtonian fluids. The fluids which don't flow by obeying Newton's law are called non Newtonian fluids. There exists friction between the layers of the fluid during the flow and it is called viscosity. There will be shear stress induced between the layers due to this friction and due to this stress, the shear force will be generated and that force will depend upon the area of cross section of the surface and coefficient of viscosity and velocity gradient i.e rate of change of velocity with respect to the displacement.
That force is given as FV=−ηAdvdx{F_V} = - \eta A\dfrac{{dv}}{{dx}}
Where ‘A’ is the area of cross section of liquid layer and dvdx\dfrac{{dv}}{{dx}} is the velocity gradient and η\eta is the coefficient of viscosity.
In the question it is given as A=1A = 1and dvdx=1\dfrac{{dv}}{{dx}} = 1
FV=−ηAdvdx{F_V} = - \eta A\dfrac{{dv}}{{dx}}
\eqalign{ & \Rightarrow {F_V} = - \eta (1)(1) \cr & \Rightarrow {F_V} = - \eta \cr}
Negative sign indicates that force is opposite to the velocity gradient.
Hence option C will be the correct answer.

Note:
Here when we go away from the axis the velocity keeps on decreasing and by the time the liquid reaches the surface liquid velocity will be very less due the more friction between the container surface and the liquid layer.