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Which one of the following equation are considered gravity and pressure force only?
- a)Stokes equation
- b)Euler equation
- c)Both a and b
- d)Neither a nor b
Correct answer is option 'B'. Can you explain this answer?
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Which one of the following equation are considered gravity and pressur...
Concept
Euler's equation of Motion
- Euler's equation for a steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure, and density of a moving fluid.
- It is based on Newton's Second Law of Motion.
- The integration of the equation gives Bernoulli's equation in the form of energy per unit weight of the following fluid.
- Euler equation of motion in which the forces due to gravity and pressure are taken into consideration
Assumptions:
- The fluid is non-viscous (i,e., the frictional losses are zero)
- The fluid is homogeneous and incompressible (i.e., the mass density of the fluid is constant)
- The flow is continuous, steady and along the streamline
- The velocity of the flow is uniform over the section
- No energy or force (except gravity and pressure forces) is involved in the flow
Stokes Law:
- According to Stokes law, the backward viscous force acting on a small spherical body of radius 'r' moving with uniform velocity V through the fluid of viscosity η is given by
F = 6 π η r V
Where η = Coefficient of viscosity, r = radius of the sphere, and V= Velocity
From above it is clear that, the viscous drag force as F = – 6πηav called Stokes' Law. Therefore option 3 is correct.
- From the figure, it is clear that the drag force fd is in the opposite direction fg
- Stoke's law is applicable for spherical particles only. The fine clay particles are not spherical in shape.
- While applying Stoke's law, the concept of equivalent diameter is used. The equivalent diameter of a soil particle is defined as the diameter of an imaginary sphere that has the same specific gravity as the soil particle and settles with the same terminal velocity as that of the soil particle.
Applications of Stoke's Law
- To calculate the terminal velocity of a falling sphere and hence the viscosity of the fluid.
- Desilting river flow
- Separating the coolant from metal chips in machining operations
- Sanitary engineering - treatment of raw water and sewerage etc.
Important Points
Reynolds equation is given by
Note: By neglecting viscous force and force due to turbulence,
Euler’s equation, max = (fg)x + (fp)x
Euler’s equation, max = (fg)x + (fp)x
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Which one of the following equation are considered gravity and pressure force only?a)Stokes equationb)Euler equationc)Both a and bd)Neither a nor bCorrect answer is option 'B'. Can you explain this answer?
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