What is Stokes law and derive terminal velocity?
What is Stokes law and derive terminal velocity?
Solution : According to stokes law, the backward viscous force acting on a small spherical body of radius r moving with velocity v through fluid of viscosity `eta`is given by ` F = 6 x eta r v`. Terminal velocity is the maximum Uniform velocity of the spherical body moving in a fluid.
What is terminal velocity derive an expression for it with a neat diagram?
# The maximum constant velocity acquired by a body while falling through a viscous medium is called its Terminal Velocity. # It is attained when force of resistance of a medium is equal and opposite to the force of gravity.
Is air resistance linear or quadratic?
The quadratic contribution is ten million times smaller and hence negligible, so there is no need to calculate the quadratic term; the air resistance is purely linear.
What is quadratic in physics?
The quadratic form is an equation in which the highest exponent of a variable is two – the square of that variable.
How do you find the acceleration of a quadratic equation?
Method 1: Using the position data (distance versus time graph). So, 1/2 a = 1.412 so then a is 2*1.412 =2.824 – thus we have obtained the acceleration from the position graph.
How do you find initial velocity with derivatives?
Velocity is the derivative! Velocity is the derivative! Initial velocity is when t = 0. s'(t) = 160 – 32t s'(t) = 160 – 32t s'(3) = 160 – 32(3) = 64 ft/sec s'(0) = 160 – 32(0) = 160 ft/sec The rock is going up, since the velocity is positive.
What is the formula to find initial velocity?
How do you find initial velocity? Work out which of the displacement (S), final velocity (V), acceleration (A) and time (T) you have to solve for initial velocity (U). If you have V, A and T, use U = V – AT. If you have S, V and T, use U = 2(S/T) – V.
What is Stokes law for settling velocity?
According to Stokes’ law, the particle sedimentation velocity is proportional to the density difference between the solid phase and the liquid phase, inversely proportional to the viscosity of the liquid, and proportional to the square of particle diameter.
What is the derivation of Stokes law?
Note:Stoke’s law is derived from the forces acting on a small particle as it sinks through the liquid column under the influence of gravity. A viscous fluid is directly proportional to the velocity and the radius of the sphere, and the viscosity of the fluid when the force that retards a sphere is moving.
What is terminal velocity state Stokes law and derive an expression for terminal velocity?
What is the expression for terminal velocity class 11th?
Terminal velocity is attained when Force of resistance = force due to gravitational attraction. 6πηrv = densityxVg (Because density=m/V), density=ρ – σ where ρ and σ are the densities of the sphere and the viscous medium resp.
What is the relationship between drag force and velocity?
Drag force is proportional to the velocity for low-speed flow and the squared velocity for high speed flow, where the distinction between low and high speed is measured by the Reynolds number.
What is quadratic drag?
As mentioned, the drag equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000). This is also called quadratic drag.
What is the quadratic velocity equation (1)?
This is a quadratic equation of the form a 2x + bx + c = 0, whose roots are given by. Making the following substitutions and choosing the relevant (saturable) root gives us: This is the quadratic velocity equation, sometimes also called the tight-binding equation or the Morrison equation (1).
How do you find the derivation of a quadratic equation?
Derivation of Quadratic Formula. The roots of a quadratic equation ax2 + bx + c = 0 is given by the quadratic formula. x = − b ± b 2 − 4 a c 2 a. The derivation of this formula can be outlined as follows: Divide both sides of the equation ax2 + bx + c = 0 by a.
What is the origin of the quadratic equation x^2 + bx + c?
It stems from the fact that any quadratic function or equation of the form y = a {x^2} + bx + c can be solved for its roots. The “roots” of the quadratic equation are the points at which the graph of a quadratic function (the graph is called the parabola) hits, crosses or touches the x-axis known as the x -intercepts.
How do you find the square root of a quadratic equation?
Here we go…. Step 1: Let y = 0 in the generic quadratic function y = ax2 + bx + c. Step 2: Move the constant “c” to the right side of the equation by subtracting both sides by “c“. Step 3: Divide the entire equation by the coefficient of the squared term which is “a“.