## Stokes’ Law Calculator

## FAQs

**How do you calculate Stokes law?** Stokes’ law is used to calculate the drag force acting on a small sphere moving through a viscous fluid. The formula for calculating this drag force is:

**F = 6πηrv**

Where:

**F**is the drag force (in Newtons, N).**η**(eta) is the dynamic viscosity of the fluid (in Pascal-seconds, Pa·s or N·s/m²).**r**is the radius of the sphere (in meters, m).**v**is the velocity of the sphere relative to the fluid (in meters per second, m/s).

**What is the Stokes law of centrifuge?** The Stokes law of centrifuge is not a commonly recognized term. Centrifugation is a process where particles in a fluid are separated by spinning them at high speeds in a centrifuge machine. While Stokes’ law can be applied to calculate the settling of particles in a centrifuge tube due to gravity, it’s not typically referred to as the “Stokes law of centrifuge.”

**How do you calculate Stokes velocity?** Stokes velocity is the terminal velocity reached by a particle falling through a viscous fluid under the influence of gravity. To calculate it, you can use the formula:

**v = (2r²(ρp – ρf)g) / (9η)**

Where:

**v**is the Stokes velocity (in meters per second, m/s).**r**is the radius of the particle (in meters, m).**ρp**is the density of the particle (in kilograms per cubic meter, kg/m³).**ρf**is the density of the fluid (in kilograms per cubic meter, kg/m³).**g**is the acceleration due to gravity (approximately 9.81 m/s²).**η**is the dynamic viscosity of the fluid (in Pascal-seconds, Pa·s or N·s/m²).

**What is the Stokes diameter formula?** The Stokes diameter (also known as the Stokes radius) is used to describe the effective size of a particle settling in a viscous fluid. It is calculated using the formula:

**D = 2r**

Where:

**D**is the Stokes diameter (in meters, m).**r**is the radius of the particle (in meters, m).

**How is Stokes shift calculated?** The Stokes shift refers to the difference in wavelength between the absorption and emission spectra of a molecule or particle. It can be calculated as:

**Stokes Shift = λ_emission – λ_absorption**

Where:

**λ_emission**is the wavelength of emitted light.**λ_absorption**is the wavelength of absorbed light.

**What is the Stokes law of droplet size?** There isn’t a specific “Stokes law of droplet size.” However, Stokes’ law can be applied to estimate the settling velocity of droplets in a liquid medium, which depends on factors like droplet size, density, and viscosity of the medium.

**How do you calculate centrifugation time?** Centrifugation time depends on several factors, including the type of centrifuge, the desired separation, and the properties of the particles or substances being separated. There is no single formula to calculate centrifugation time, but it is typically determined empirically through experimentation or by following guidelines provided by the manufacturer of the centrifuge.

**What is the Stokes law for dummies?** Stokes’ law, in simple terms, describes how small particles or objects move through a thick, viscous fluid (like a liquid) due to the force of gravity. It tells us that the drag force experienced by these particles is proportional to their size, velocity, and the viscosity of the fluid.

**Is Stokes law only for laminar flow?** Stokes’ law is primarily applicable to particles moving through a fluid in a regime of laminar flow, where fluid layers move smoothly and parallel to each other. In turbulent flow, the application of Stokes’ law becomes less accurate because turbulent flow involves complex eddies and irregular fluid motion.

**What is an example of Stokes law?** An example of Stokes’ law is a small solid particle, like a dust particle, falling slowly through a viscous liquid, such as oil or syrup. Stokes’ law can be used to estimate the terminal velocity at which the particle settles in the liquid due to the force of gravity.

**What does Stokes equation tell us?** The Stokes equation tells us how the drag force acting on a small sphere moving through a viscous fluid depends on the sphere’s size, velocity, and the viscosity of the fluid. It provides a mathematical description of this drag force, which is essential for understanding the motion of particles in viscous media.

**What is Stokes velocity?** Stokes velocity is the terminal velocity reached by a small particle falling through a viscous fluid under the influence of gravity. It is the maximum velocity that the particle can attain, and it depends on the size of the particle, the density of the particle and the fluid, the gravitational acceleration, and the viscosity of the fluid.

**What is the formula for flow rate velocity diameter?** The formula for flow rate can be expressed as:

**Q = A * v**

Where:

**Q**is the flow rate (in volume per unit time, such as cubic meters per second, m³/s).**A**is the cross-sectional area through which the fluid flows (in square meters, m²).**v**is the velocity of the fluid (in meters per second, m/s).

The diameter is not explicitly included in this formula, but it can be related to the cross-sectional area through the formula A = π * (d/2)², where **d** is the diameter of the pipe or conduit.

**What is the unit of Stokes shift?** The unit of Stokes shift is typically expressed in nanometers (nm) or wavenumbers (cm⁻¹) when measuring the difference in wavelength between the absorption and emission spectra of a molecule or particle.

**What is an example of a Stokes shift?** An example of a Stokes shift is when a fluorescent molecule absorbs light at one wavelength (e.g., blue light at 450 nm) and then emits light at a longer wavelength (e.g., green light at 525 nm). The Stokes shift in this case would be 525 nm – 450 nm = 75 nm.

**What is the Stokes shift?** The Stokes shift is the difference in wavelength between the absorbed and emitted light by a fluorescent or luminescent material. It indicates the energy lost during the relaxation process of excited molecules, resulting in longer-wavelength emission.

**What is the Stokes number of a droplet?** The Stokes number (St) of a droplet is a dimensionless number used to determine the behavior of particles or droplets in a fluid flow. It relates the response time of a particle to the characteristic time scale of the flow. The formula for the Stokes number is:

**St = (ρp * d² * U) / (18η)**

Where:

**St**is the Stokes number.**ρp**is the density of the particle or droplet.**d**is the diameter of the particle or droplet.**U**is the characteristic velocity of the fluid flow.**η**is the dynamic viscosity of the fluid.

**What is the formula for drop size?** The formula for drop size typically depends on the context, such as the method used for measuring or characterizing drop size. Common methods for determining drop size include laser diffraction, microscopy, or other image analysis techniques. The formula may vary based on the specific equipment and methodology used.

**How do you determine the size of a droplet?** The size of a droplet can be determined using various techniques, including laser diffraction, microscopy, or image analysis. The specific method chosen depends on the characteristics of the droplets and the level of precision required.

**How do you calculate centrifuge?** Calculating the performance of a centrifuge involves various parameters, such as rotor speed, rotor size, particle size, and density. There isn’t a single formula to calculate centrifuge performance, as it depends on the specific application and goals. Manufacturers often provide guidelines, and calculations may involve considerations like relative centrifugal force (RCF) or gravitational force.

**How do you calculate centrifugation force?** Centrifugation force can be calculated using the formula for relative centrifugal force (RCF):

**RCF = (r * (ω²)) / g**

Where:

**RCF**is the relative centrifugal force (in g or times gravity).**r**is the distance from the center of rotation to the particle (in meters, m).**ω**is the angular velocity of the centrifuge rotor (in radians per second, rad/s).**g**is the acceleration due to gravity (approximately 9.81 m/s²).

**How is centrifugation measured?** Centrifugation is measured in terms of relative centrifugal force (RCF) or revolutions per minute (RPM) of the centrifuge rotor. RCF is a more accurate measure of the force experienced by particles in a centrifuge because it takes into account the rotor radius and angular velocity.

**What are the limitations of Stokes law?** The limitations of Stokes’ law include:

- Applicability to small, spherical particles: It’s primarily applicable to small, spherical particles moving at low Reynolds numbers in viscous fluids.
- Laminar flow assumption: It assumes laminar flow, which may not be accurate for turbulent flow conditions.
- Neglect of particle interaction: Stokes’ law does not account for interactions between particles, which can occur in concentrated suspensions.
- Limited to dilute suspensions: It is most accurate for dilute suspensions, where particle-particle interactions are minimal.
- Spherical shape assumption: The law assumes that particles are perfectly spherical, which may not be true for irregularly shaped particles.

**What are two applications of Stokes law?** Two applications of Stokes’ law include:

- Particle settling: It is used to estimate the settling velocity of small particles in a fluid, which is important in sedimentation processes and particle separation.
- Particle characterization: It can be used to determine the size of particles, such as in particle size analyzers that utilize Stokes’ law principles.

**What flow is Stokes law valid for?** Stokes’ law is valid for flows characterized by low Reynolds numbers, which are typically associated with laminar flow. It is not accurate for turbulent flow conditions where fluid motion is chaotic and irregular.

**Why is Stokes important?** Stokes’ law is important because it provides a fundamental understanding of how small particles move through viscous fluids under the influence of gravity. It is used in various scientific and engineering applications, such as particle sedimentation, particle characterization, and the study of fluid dynamics in low Reynolds number environments.

**How can we determine whether the flow is laminar or turbulent?** The flow regime (laminar or turbulent) can be determined using the Reynolds number (Re), which is a dimensionless number that quantifies the relative importance of inertial forces to viscous forces in a fluid flow. The Reynolds number is calculated as:

**Re = (ρ * v * L) / η**

Where:

**Re**is the Reynolds number.**ρ**is the density of the fluid.**v**is the velocity of the fluid.**L**is a characteristic length (such as the diameter of a pipe).**η**is the dynamic viscosity of the fluid.

If Re < 2,000, the flow is typically laminar, while if Re > 4,000, the flow is usually turbulent. For values between 2,000 and 4,000, the flow is considered a transition zone and may exhibit characteristics of both laminar and turbulent flow.

**What is the conclusion of the Stokes law?** The conclusion of Stokes’ law is that it provides a mathematical description of the drag force experienced by small spherical particles moving through a viscous fluid under the influence of gravity. It helps us understand the behavior of such particles and is valuable in various scientific and engineering applications.

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