# Fluid flow between parallel plates

• hamurabi
In summary: So, you need to multiply the shear stress by the area of the plate in contact with the fluid. This will be given by: $$F=\tau A = 0.0356 (0.3)=0.01068\ N$$In summary, the velocity distribution for laminar flow between parallel plates is given by u/umax = 1-(2y/h)2, where h is the distance separating the plates and the origin is placed midway between the plates. For flow of water at 15 0C with maximum speed of umax=0.05 m/s and h=5 mm, the force on a 0.3 m2 section of the lower plate is 0.01068
hamurabi

## Homework Statement

The velocity distribution for laminar flow between parallel plates is given by
u/umax = 1-(2y/h)2
where h is the distance separating the plates and the origin is placed midway between the plates.
Consider flow of water at 15 0C with maximum speed of umax=0.05 m/s and h=5 mm. Calculate the
force on a 0.3 m2 section of the lower plate and give its direction.

## Homework Equations

Given in the problem and perhaps P = F/A

## The Attempt at a Solution

Well I know that the maximum velocity will occur at the origin i.e y=0 and that the velocity at the plates is zero. So the maximal force would occur also at the origin - Would I have to get the y-component of the velocity?

I am guessing that the temperature is given so that we can get density (0.999) and viscosity (1.78 cp) from tables - or this may just be a red herring

Now the thing I am having problems with is linking the velocity with an equation to get pressure so that I can calculate the force.

Any guidance would be much appreciated!

hamurabi said:

## Homework Statement

The velocity distribution for laminar flow between parallel plates is given by
u/umax = 1-(2y/h)2
where h is the distance separating the plates and the origin is placed midway between the plates.
Consider flow of water at 15 0C with maximum speed of umax=0.05 m/s and h=5 mm. Calculate the
force on a 0.3 m2 section of the lower plate and give its direction.

## Homework Equations

Given in the problem and perhaps P = F/A

## The Attempt at a Solution

Well I know that the maximum velocity will occur at the origin i.e y=0 and that the velocity at the plates is zero. So the maximal force would occur
also at the origin - Would I have to get the y-component of the velocity?
The maximum velocity will occur at the plates, not at y = 0. The shear rate of the fluid is given by $$\frac{du}{dy}=-u_{max}\frac{4y}{h^2}$$At the lower plate, y =-h/2, the shear rate is $$\frac{du}{dy}=\frac{2u_{max}}{h}=20\ s^{-1}$$
hamurabi said:
I am guessing that the temperature is given so that we can get density (0.999) and viscosity (1.78 cp) from tables - or this may just be a red herring
If the viscosity is1.78 cp, this means that the shear stress at the lower plate is: $$\tau=\eta \frac{du}{dy}=0.0178 (20)=0.356\ dynes/cm^2=0.0356\ Pa$$
hamurabi said:
Now the thing I am having problems with is linking the velocity with an equation to get pressure so that I can calculate the force.

Any guidance would be much appreciated!
They are asking for the shear force, not the normal force.

## 1. What is fluid flow between parallel plates?

Fluid flow between parallel plates is a type of laminar flow in which a fluid, such as a liquid or gas, moves between two flat plates that are parallel to each other. This flow is characterized by smooth, orderly movement of the fluid particles in parallel layers, with minimal mixing or turbulence.

## 2. What factors affect fluid flow between parallel plates?

The factors that affect fluid flow between parallel plates include the viscosity of the fluid, the distance between the plates, the pressure difference across the plates, and the presence of any external forces such as gravity or an electric field. These factors can influence the velocity and direction of the fluid flow.

## 3. How is fluid flow between parallel plates described mathematically?

Fluid flow between parallel plates can be described mathematically using the Navier-Stokes equations, which are a set of partial differential equations that describe the motion of a viscous fluid. These equations take into account factors such as pressure, viscosity, and velocity to predict the behavior of the fluid flow.

## 4. What is the difference between laminar and turbulent flow between parallel plates?

In laminar flow between parallel plates, the fluid particles move in parallel layers with minimal mixing or disruption. In turbulent flow, the fluid particles move in a chaotic, random pattern and there is more mixing and energy dissipation. The transition from laminar to turbulent flow can occur at a critical Reynolds number, which is dependent on the fluid properties and plate geometry.

## 5. How is fluid flow between parallel plates used in practical applications?

Fluid flow between parallel plates has many practical applications, such as in heat exchangers, where it is used to transfer heat between two fluids. It is also used in the design of airplane wings and car bodies to reduce drag and improve aerodynamics. In microfluidic devices, fluid flow between parallel plates is used to manipulate and control small volumes of fluids for various purposes, such as chemical analysis or drug delivery.

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