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Properties-of-fluid

The general relation between shear stress and velocity gradient of fluid can be written as: `tau=A ((du)/(dy))^n+B` Where A , B and n are constants that depend upon type of fluid and condition imposed on flow. Comment value of se constants so that fluid may behave as:
  • An ideal fluid
  • A newtonian fluid
  • A non newtonian fluid
Also indicate wher fluid with following characteristics is Newtonian or non-Newtonian.
  • `tau=A*y+B` and `U=C_1+C_2*y+C_3*y^2`
  • `tau=A*y^(n (n-1))` and `U=C*y^n`

Solution:

Given,

`tau=A ((du)/(dy))^n+B`

IDEAL FLUID:

Since an ideal fluid has zero viscosity (i.e, shear stress is always zero regardless of the motion of the fluid), we have,

`A=B=0`

A NEWTONIAN FLUID:

Since a newtonian fluid follows the newtons law of viscosity, `tau=mu*(du)/(dy)`, therefore compairing, we get,

`n=1`,

`A=mu`,

`B=0`

Air,water,kerosine etc behaves as Newtonian fluid under normal working conditions. 


A NON-NEWTONIAN FLUID:

Depending upon the value of power index `n`, the  non-Newtonian fluid are classified as:

  • If `n>1` and B=0, Dilatent fluid. Example: sugar solution, aqueous suspension and printing ink.

  • If `n<1` and B=0, Pseudo-plastic fluid.  Example: Blood, milk, liquid cement and clay.

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A vertical excavation was made in a clay deposit having weight of 20 KN/`m^3`. It caved in after the depth of digging reached 4m. Taking angle of internal friction to be zero, calculate the value of cohesion. If the same clay is used as a backfill against a retaining wall upto a height of 8m, Calculate:
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The general relation between shear stress and velocity gradient of fluid can be written as: `tau=A ((du)/(dy))^n+B` Where A , B and n are constants that depend upon type of fluid and condition imposed on flow. Comment value of se constants so that fluid may behave as:
  • An ideal fluid
  • A newtonian fluid
  • A non newtonian fluid
Also indicate wher fluid with following characteristics is Newtonian or non-Newtonian.
  • `tau=A*y+B` and `U=C_1+C_2*y+C_3*y^2`
  • `tau=A*y^(n (n-1))` and `U=C*y^n`

A plate having an area of `0.6 m^2` is sliding down the inclined plane at an angle of `30^0` to the horizontal with a velocity of 0.36 m/sec. There is a cushion of fluid 1.8 mm thick between the plane and the plate. Find the viscosity of the fluid if the weight of the plate is 280N.

The general relation between shear stress and velocity gradient of fluid can be written as: `tau=A ((du)/(dy))^n+B` Where A

B and n are constants that depend upon the type of fluid and condition imposed on the flow. Comment the value of these constants so that the fluid may behave as: An ideal fluid A newtonian fluid A non newtonian fluid Also indicate whether the fluid with the following characteristics is Newtonian or non-Newtonian. `tau=A*y+B` and `U=C_1+C_2*y+C_3*y^2` `tau=A*y^(n (n-1))` and `U=C*y^n`

Properties of fluid

Fluid-Mechanics