How is viscous drag calculated?
Fs = 6πrηv, where r is the radius of the object, η is the viscosity of the fluid, and v is the object’s velocity.
How was the drag equation derived?
The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object. size of the body, expressed in terms of its wetted area A, and. drag force Fd.
How do you derive Stokes formula?
Stokes Law Derivation
- F ∝ ηa rb vc.
- F = K * ηa rb vc ……….. (
- [MLT-2] = [[ML-1T-1]a . Lb . [ LT-1]c ]
- [MLT-2] = [Ma ] [L-a+b+c] [T-a-c]
- a = +1 ……………..(
- -a+b+c = +1 …………….. (
- -a-c= -2 ……………..(
- F = K * η1 r1 v1 = K ηrv.
What is Stokes law and its derivation?
The law is derived considering the forces acting on a particular particle as it sinks through the liquid column under the influence of gravity. The force that retards a sphere moving through a viscous fluid is directly proportional to the velocity and the radius of the sphere, and the fluid’s viscosity.
How do you derive Stokes drag?
He found what has become known as Stokes’ Law: the drag force F on a sphere of radius a moving through a fluid of viscosity η at speed v is given by: F=6πaηv. Note that this drag force is directly proportional to the radius.
What is viscous drag?
viscous drag: a resistance force exerted on a moving object, with a nontrivial dependence on velocity terminal speed: the speed at which the viscous drag of an object falling in a viscous fluid is equal to the other forces acting on the object (such as gravity), so that the acceleration of the object is zero.
How do you find the drag form?
The drag equation states that drag D is equal to the drag coefficient Cd times the density r times half of the velocity V squared times the reference area A. For given air conditions, shape, and inclination of the object, we must determine a value for Cd to determine drag.
What is B in drag equation?
where C is the drag coefficient, A is the area of the object facing the fluid, and ρ is the density of the fluid. (Recall that density is mass per unit volume.) This equation can also be written in a more generalized fashion as FD=bv2, where b is a constant equivalent to 0.5CρA.
Who derived the drag equation?
Rayleigh “derived” the drag equation in On the Resistance of Fluids, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Ser. 5, v.
What is viscous drag force?
What do you mean by viscosity derive expression for it?
The SI unit of viscosity is N ⋅ m/[(m/s)m^2 ] = (N/m^2)s or Pa ⋅ s . From equation 1, we can say that the effort required to move a fluid (like pouring) depends on its viscous nature, labelled by η or coefficient of viscosity.
How do you calculate the force of a viscous drag?
For viscous drag, the formula for the force is, $$ \\mathbf F=\\pm\\eta A\ abla\\mathbf u $$ where $\\eta$ is the viscosity coefficient, $A$ the area and $\ abla\\mathbf u$ the velocity gradient.
Is the drag force equation constructive or destructive?
The drag force equation is a constructive theory based on the experimental evidence that drag force is proportional to the square of the speed, the air density and the effective drag surface area.
How do you derive the drag coefficient?
The drag coefficient is simply the proportionality constant that relates drag force to these factors for a given object, so there is no way to ‘derive’ it other than by experiment. But there is also the theory of the linear dependency of drag force on the velocity of the falling object. Can you explain that bit as well? Linear dependence??
What is k in Stoke’s law viscosity equation?
From Stoke’s Law viscosity equation, we know that viscous force acting on a sphere is directly proportional to the following parameters: Now let us evaluate the values of a, b and c. Here, k is the constant of proportionality which is a numerical value and has no dimensions.