Properties of Fluids - 1 - GATE ME Fluid Mechanics Free MCQ Test with solutions

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The specific gravity of a liquid is the ratio of two similar quantities (densities) which makes it unitless.

for the given problem, L, D, μ and fare constant

• A perfect fluid is incompressible and frictionless and it is explained with the help of Euler's equation.

Euler's equation of motion:

• The 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 which states that if the external force is zero, linear momentum is conserved.
• The integration of the equation gives Bernoulli's equation in the form of energy per unit weight of the following fluid.

It is based on the following 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.

• The concept of the continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables.
• In this approach, the matter is continuously distributed with no void present continuum concept be applied if the mean free path is much less than the system dimensions.
• Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.
• Describing a fluid flow quantitatively makes it necessary to assume that flow variables (pressure, velocity etc.) and fluid properties vary continuously from one point to another. 
• One of the factors considered important in determining the validity of the continuum model is molecular density. It is the distance between the molecules which is characterized by a mean free path ( λ ). It is calculated by finding statistical average distance the molecules travel between two successive collisions.
• If the mean free path is very small as compared with some characteristic length in the flow domain (i.e., the molecular density is very high) then the gas can be treated as a continuous medium.
• If the mean free path is large in comparison to some characteristic length, the gas cannot be considered continuous and it should be analysed by the molecular theory.
• A dimensionless parameter is known as Knudsen number, K_n = λ/L, where λ is the mean free path and L is the characteristic length. It describes the degree of departure from the continuum.
• Usually when Kn > 0.01, the concept of the continuum does not hold good and when Kn < 0.01, the concept of the continuum does hold good.
• In the continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. can be expressed as continuous functions of space and time.

• A solid can resist shear stress by a static deformation; a fluid cannot
• Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid
• The fluid moves and deforms continuously as long as the shear stress is applied
• So, a fluid at rest must be in a state of zero shear stress

When a real fluid flows past a solid boundary, a layer of fluid which comes in contact with the boundary surface adheres to it on account of viscosity. Since this layer of fluid cannot slip away from the boundary surface it attains the same velocity as that of the boundary.

In other words, at the boundary surface there is no relative motion between the fluid and the boundary. This condition is known as the no slip condition.

∴ The condition of "No-slip" at rigid boundaries is applicable to flow if all real fluids.