Mechanics of Fluid - short answer questions (AMIE Winter 2020)

Explain the following in brief (5 x 4)

Specific weight and specific volume of a fluid

Specific weight, sometimes referred to as unit weight, is simply the weight of fluid per unit volume. It is usually denoted by the Greek letter γ (gamma) and has dimensions of force per unit volume.
Its units in the SI system are N/m³ or kg/m²sec² 

Specific volume is the volume of a unit mass of a substance. In other words, it is the ratio of a substance’s volume to its mass. The unit of measurement is (m³/kg).

Buoyancy and centre of buoyancy

Buoyancy is an upward force exerted by a fluid on an immersed object in a gravity field. In fluids, pressure increases with depth. Hence, when an object is immersed in a fluid, the pressure exerted on its bottom surface is higher than the pressure exerted on its top surface.
This difference in pressure leads to a net upward force (buoyancy force).
Buoyancy force will act through the centre of gravity of the displaced fluid and that point i.e. centre of gravity of the displaced fluid will be termed as centre of buoyancy. Therefore, we can define the term centre of buoyancy as the point through which the force of buoyancy is supposed to act.

Centre of buoyancy = Centre of gravity of the displaced fluid = Centre of gravity of the portion of the body immersed in the liquid

Streamline and streak line

  • It is an imaginary line showing the positions of various fluid particles.
  • Particles may change streamline depending on the type of flow
  • Streamlines cannot intersect with each other, they are always parallel.
  • No flow across streamline. 

Streak Line

  • It is a real line showing instantaneous positions of various particles.
  • May change from instant to instant.
  • Streak line changes with time. Two streak lines may intersect each other.
  • Flow across the streak line is possible.

Reynold’s number and Mach number

Reynolds Number
The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorize the fluids in systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. Mathematically, the Reynolds number, Re, is defined as

Re = ρvd/μ
ρ = density
v = velocity
d  = diameter
μ = viscosity

Mach Number
Mach number is used to compare the speed of any object with the speed of sound. It is mainly used to know the proper idea of the motion of aeroplanes and rockets. Mach number is a dimensional less quantity expressing the ratio of the velocity of an object in a medium to the speed of sound. 

Classification of Mach Number 
According to the variation of Mach number, fluid flow is classified.
  • Subsonic: The Mach number remains below 0.8 in subsonic flow. Commercial aeroplanes flowing in this range have a round nose and leading edges.
  • Sonic: The Mach number is one in sonic flow. In these types of flow, the velocity of an object is equal to the velocity of sound in the local medium.
  • Supersonic: If an object is flowing with greater velocity than the sound, it is said to have supersonic velocity. It has a Mach number greater than one. Aeroplanes have proper designs to undergo supersonic speed.
  • Hypersonic: If the speed of an object is higher than the speed of sound, then the flow is called hypersonic. In this type of flow, the Mach number is five to ten.
Mach number is represented with the symbol ‘M’.

Mach Number= Speed of object / Speed of sound

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