PPT on fully Mathematical Derivation of Viscous Flow as part of FLUID MECHANICS by M.M.RAFIK.
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Subject Code : 130101
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Transcript of PPT on fully Mathematical Derivation of Viscous Flow as part of FLUID MECHANICS by M.M.RAFIK.
Subject Code : 130101
Topic:
Viscous Flow
3rd semester
B.E. Mechanical
CCET, WADHWAN
Flow of Viscous fluid between two Parallel Plate.
CCET, WADHWAN
For Steady & Uniform Flow acceleration is Zero. Net Force F = mass X Acceleration = 0
CCET, WADHWAN
Velocity Distribustion
Shear Stress
Put Value of shear stress in eq.
CCET, WADHWAN
CCET, WADHWAN
CCET, WADHWAN
Ratio of Maximum Velocity to Avg. Velocity
Velocity Will be maximum at Y = t/2,
CCET, WADHWAN
Integrating from 0 to t
CCET, WADHWAN
Ratio of maximum Velocity to Avg. velocity
CCET, WADHWAN
Drop of Pressure Head for a given Length
Avg. Velocity is given by
Integrate With respect to X
CCET, WADHWAN
CCET, WADHWAN
Shear Stress Distribution
CCET, WADHWAN
Journal Bearing
A journal Bearing is a hollow cylindrical enclosing a solid shaft that rotates about its axis at radial speed.
The gap between bearing and shaft is filled by viscous oil and it will be consider at rest.
CCET, WADHWAN
Consider a Shaft Diameter = D Length of shaft = L Clearance = t
CCET, WADHWAN
Torque required to overcome viscous resistance
Power Absorbed
CCET, WADHWAN
Foot Step Bearing
When a vertical shaft is required to rotate inside a fixed bearing, the viscous oil is placed between the top of the bearing and bottom of the shaft.
R = Radius of shaft N = Speed of the shaft X= Clearance between
Bearing shaft
CCET, WADHWAN
CCET, WADHWAN
CCET, WADHWAN
Power absorbed to overcoming the shear resistance
CCET, WADHWAN
Movement of Piston in Dashpot
Dashpot is a device used for damping vibration of machine by using high viscous fluid.
It consist of a piston which moves in a cylinder. Diameter of cylinder is slightly greater the piston. Piston is connected to the machine element whose
movement is to be restrained. Consider a piston moving in a vertical dashpot
containing oil as shown in fig.
CCET, WADHWAN
CCET, WADHWAN
The oil flow through the clearance behaves as laminar flow between parallel plates.
Pressure difference for parallel plate is given by
CCET, WADHWAN
Eq. Shows that piston velocity is directly proportional to load acting on the piston.
CCET, WADHWAN
Methods of Measurement of Viscosity
The device use for measurement of viscosity are known as Viscometer.
Various Methods for Measurement of Viscosity
I. Capillary tube Method
II. Rotating cylinder Method
III. Falling Sphere Method
IV. Orifice tube Viscometer
CCET, WADHWAN
Capillary tube Method
This method use Hagen- Poiseuille eq. for laminar flow through circular pipe.
A tank in which the liquid is filled whose viscosity is to be determined.
CCET, WADHWAN
CCET, WADHWAN
CCET, WADHWAN
Rotating Cylinder Method
Rotating Cylinder Method of measuring viscosity is based on Newton’s law of Viscosity.
CCET, WADHWAN
CCET, WADHWAN
Which is final equation.
Thank you….
