Variables needed for getting dimensionless groups
In almost of the fluid phenomena the next variables may live important - Length. L
- Acceleration due to gravity, g
- Mass density, ρ
- Velocity, V
- Pressure, p
- Viscosity, µ
- Surface tension, σ
-Velocity of audio CForces needed to run the Dimensionless Numbers inwards Fluid Mechanics
The next forces tin post away live formed from these variables. Inertia forcefulness = mass x acceleration = ρL3 x(V/t)= ρL2V x(L/t)= ρL2V2 Viscous forcefulness = surface area X shear stress = L2 x µ x (V/L) = µVL Gravity Force = mass X acceleration due to gravity = ρL3g Pressure Force = pressure level x surface area = pL2
Elastic Force = mass modulus of elasticity X surface area = eastward x L2 = ρC2L2, Since eastward = ρC2
Surface Tension Force = σL
The next dimensionless groups tin post away live formed past times combining inertia forcefulness alongside each of the independent forces.
Reynolds Number inwards Fluid Mechanics, NRe
It is the ratio of inertia forcefulness in addition to pasty force.
Reynolds publish formula, NRe = Inertia forcefulness / Viscous forcefulness = ρL2V2 / µVL = ρVL/µ
So , Reynolds publish equation = ρVL/µ . For getting Reynold Number using kinematic viscosity nosotros accept to dissever the dynamics viscosity µ past times the density ρ.
Reynolds publish similarity is used when pasty forcefulness is predominant. For example, catamenia through pipes completely submerged flow, catamenia through venturimeter in addition to orificemeter etc.
Froude Number, Fr
It is the ratio of inertia forcefulness to gravity force.
Froude Number , Fr = Inertia Force / Gravity Force = ρL2V2 / ρL3g = V2/Lg
Froude publish is used when gravitational forcefulness is predominant inwards the fluid motion. For instance opened upward channel flow, moving ridge displace inwards the ocean, forces on couple piers in addition to off shore structures.
Euler Number , E
It is the ration of pressure level forcefulness in addition to inertia force.
Euler Number = Pressure forcefulness / Inertia Force = pL2 / ρL2V2 = p/ρV2 = F/ ρV2L2
Euler publish is of import when pressure level forcefulness is predominant. For example, catamenia through pipes, catamenia over submerged bodies, catamenia of H2O through orifices in addition to mouthpieces etc.
Mach number, M
Square source of the ratio of inertia forcefulness to the elastic forcefulness Mach Number = (Inertia forcefulness / elastic force)1/2 = (ρL2V2 / ρC2L2)1/2 = V/C
The ratio v2/c2 is known every bit Cauchy’s number. Mach publish is of import inwards compressible fluid catamenia at high velocities. For instance high velocity catamenia inwards pipes, displace of high velocity projectiles in addition to missiles.
Weber Number, westward
It is defined every bit the ratio of inertia forcefulness to the surface tension force.
Weber Number = Inertia forcefulness / Surface tension forcefulness = ρL2V2/ σL = ρLV2/ σ
Weber publish is of import when surface tension is important. For example, capillary underground flow, droplet formation, human inwards blood catamenia etc.
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