Coefficient of Viscosity | Physical Chemistry PDF Download

What is a Viscous Gradient?

The viscous gradient is the difference in the velocity between the adjacent layer of the fluid. If more force is applied by the upper layer to move forward the more will be the viscous gradient. It is represented by v/x, where v is the velocity difference and x will be the difference of distance between the two layers. So, the higher the value of v/x, the more will be the viscous gradient. 

Coefficient of Viscosity

• The ratio of the shearing stress to the velocity gradient of the fluid is called the coefficient of viscosity η.
• Hence the coefficient of viscosity is given by,
  η  = F . d / A .ⅴ
• Where F is the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.
  ⅴ is the velocity.
  A is the area
• d is the distance between the two layers of liquid skidding over each other.
• The difference in the stream of velocity between the adjacent layers of the fluid is measured in the velocity gradient.
• The viscosity of gas is less than the liquid viscosity.

SI Unit of Coefficient of Viscosity

• Every liquid has its specific viscosity and the measure of this attribute is called the coefficient of viscosity.
• The coefficient of viscosity η is defined as the tangential force F required to maintain a unit velocity gradient between two parallel layers of liquid of unit area A.
• The SI unit of η is Newton-second per square meter (Ns. m^-2) or
• Pascal-seconds (Pa .s)
• Hence the coefficient of viscosity is a measure of the resistance of the fluid to deformation at a given rate due to internal friction.

Unit of Coefficient of Viscosity

• The centimetre-gram-second or CGS unit of coefficient of viscosity,  η is dyne-sec/ cm² which is equal to Poise.
• Where one poise is exactly 0.1 Pa·s.
• The meter-kilogram-second or MKS unit is: Kilogram per meter per second or Kg m^-1 s^-1.
• Coefficient of Viscosity Unit and Dimension
• Since, the formula for coefficient of viscosity is given by,
  η  = F . d/ A .ⅴ  =  MLT⁻² . L / L² . LT⁻¹
• On solving  we get,
  Dimensional formula for η = ML⁻¹T⁻¹ML⁻¹T⁻¹ and it is equivalent to Kg m ^-1 s ^-1

The Viscosity of Water in SI Units

• The coefficient of viscosity of water can be determined by using Poiseuille’s law.
• Poiseuille’s equation for the flow of liquid determines the volume of the liquid flowing through a capillary tube in a unit of time.
• Poiseuille's formula is given by,
  
• Here, the rate of flow of the viscous liquid through a tube of length 'l' and radius '໗' is proportional to the applied pressure P. 
• The rate of flow of the viscous liquid is proportional to the fourth power of the inner radius of the tube and inversely proportional to the viscosity of the liquid and the length of the tube. 
• The formula for the coefficient of viscosity of water is given by,
  
  
• Here, Ⅴ  is the rate of flow of the volume of liquid.
• P is the pressure that would be applied to the liquid.
• ໗ is the inner radius of the capillary tube.
• l is the length of the capillary tube.
• SI unit of viscosity of water is Ns.m^-2 or Pa.s.