Linear drag in a liquid and terminal velocity

• maxrof
In summary, the drag force experienced by an object moving through a liquid is given by D = (bv, opposite the direction of motion), where b is the drag coefficient and n is the viscosity of the liquid. For a sphere of radius R, b can be calculated as 6 pi n R. The terminal speed of a spherical particle with mass m and radius R falling through a liquid of viscosity n can be expressed as Vterm = sqrt(4mg / A), where A is the cross-sectional area of the particle. To solve for the time it takes for a 1.1mm diameter sand grain with a density of 2400 kg/m^3 to settle to the bottom of a 55m-deep lake with
maxrof

Homework Statement

An object moving in a liquid experiences a linear drag force: D =(bv, direction opposite the motion), where b is a constant called the drag coefficient. For a sphere of radius R, the drag constant can be computed as b = 6 pi n R, where n is the viscosity of the liquid.

1. Find an algebraic expression for the terminal speed Vterm of a spherical particle of radius R and mass m falling through a liquid of viscosity n.

2. Water at 20C has viscosity n = 1.0 x 10^-3N. Sand grains have density 2400 kg/m^3. Suppose a 1.1mm diameter sand grain is dropped into a 55m-deep lake whose water is a constant 20C. If the sand grain reaches terminal speed almost instantly (a quite good approximation), how long will it take the sand grain to settle to the bottom of the lake?.

Homework Equations

Vterm = sqrt(4mg / A)

D = 1/4 A v^2

Area = 2 pi r^2 [cross section of spherical particle to calculate drag]

The Attempt at a Solution

I'm puzzled where to go. I have my Vterm formula, but I don't know where the drag coefficient (b) plays into that. I've looked through my textbook a few times and I'm missing a clear explanation of how this works.

It's the hardest problem from the set (first year physics for engineers). <_____<

When the sphere attains terminal velocity, what forces balance?

What is linear drag in a liquid?

Linear drag in a liquid is a type of resistance force that acts on an object as it moves through a fluid, such as air or water. It is a result of the fluid molecules colliding with the surface of the object, creating a drag force that opposes the object's motion.

How does linear drag affect an object's motion in a liquid?

Linear drag slows down an object's motion in a liquid by exerting a force in the opposite direction of the object's movement. As the object's speed increases, so does the magnitude of the linear drag force, until it reaches a point where the drag force is equal to the object's weight. This is known as the terminal velocity.

What factors affect the amount of linear drag experienced by an object in a liquid?

The amount of linear drag experienced by an object in a liquid is affected by several factors, including the object's size, shape, speed, and the density and viscosity of the liquid. Objects with a larger surface area, such as a parachute, experience more linear drag than objects with a smaller surface area, such as a bullet.

What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid due to the balance between the object's weight and the drag force acting on it. At terminal velocity, the net force on the object is zero, and the object will continue to fall at a constant speed.

How can linear drag and terminal velocity be calculated?

The calculation of linear drag and terminal velocity involves several equations, including the drag force equation (F_d = 1/2 * ρ * v^2 * A * C_d) and the net force equation (F_net = F_g - F_d). By setting the net force equal to zero and solving for velocity, the terminal velocity can be calculated. Additionally, the amount of linear drag can be calculated by rearranging the drag force equation and solving for the drag coefficient (C_d).

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