Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today, we will discuss how pressure behaves in fluids at rest. Who can tell me what happens to shear stress in a stationary fluid?
Shear stress becomes zero, right?
Exactly! Without shear stress, only normal stress in the form of pressure acts on the fluid. Therefore, pressure is a function of the vertical position in the fluid.
Is pressure the same everywhere in a horizontal plane?
Good question! Yes, pressure remains constant across any horizontal surface under static conditions because it varies only with height.
Can you explain why it only varies vertically?
Certainly! It varies vertically due to gravitational effects acting on the weight of the fluid. The deeper you go, the greater the weight of the fluid above, resulting in increased pressure.
So we can use the equation P = ρgz to calculate pressure at a certain depth?
Exactly! And remembering that simplifies our calculations in fluid statics. Let's summarize: in a static fluid, shear stress is zero, pressure is constant in horizontal planes, and pressure increases with depth.
Next, let's talk about how we measure pressure. Does anyone know the difference between gauge pressure and vacuum pressure?
Gauge pressure is the pressure above atmospheric pressure, right?
Correct! And vacuum pressure is measured below atmospheric pressure. It’s essential to know your reference point.
So if we measure pressure in a car tire, it's gauge pressure?
Yes, because it’s measured above atmospheric pressure. Now, can anyone give an example of how we might apply this in real life?
Using a barometer to measure atmospheric pressure?
Absolutely! The mercury barometer is a classic example for measuring atmospheric pressure with a vacuum at the top of the column.
Will the height of the mercury change with altitude?
Yes! Pressure decreases with altitude, leading to lower mercury heights in barometers at higher elevations. Let’s summarize: Gauge pressure is above atmospheric, and vacuum pressure is below. And remember: atmospheric pressure changes with altitude.
Now, let’s calculate pressure at different depths using the formula P = ρgz. Who can tell me what these variables represent?
ρ is the density of the fluid, g is gravity, and z is depth.
Exactly! Let’s say we have water with a density of 1000 kg/m³ and we want to calculate the pressure 10 m underwater. Can anyone calculate this?
P = 1000 kg/m³ * 9.81 m/s² * 10 m = 98100 Pa!
Spot on! That’s the pressure at that depth. Who can tell me how this relates to our previous discussion about static pressure in horizontal planes?
The pressure remains constant across any horizontal surface, no matter where you are at that depth.
Exactly right! Summarizing today, we’ve applied P = ρgz for practical calculations and discussed pressure distribution in horizontal planes.
Pressure varies only in the vertical direction due to gravity in fluids at rest.
The equation P = ρgz is used to calculate the pressure at a specific depth in a fluid.
Gauge pressure indicates pressure above atmospheric levels, while vacuum pressure indicates below atmospheric levels.
Pressure below, pressure above, in static fluids, it’s all love.
Imagine a calm lake; the water's surface is flat. No rush, no flow, just the stillness that keeps the pressure even from its depths to its height!
PLUG - Pressure Lifts Under Gravity, reminding us pressure increases with depth in fluids.
GAP - Gauge Above Pressure, emphasizing that gauge pressure is always above atmospheric pressure.
Term
Hydrostatic Pressure
Click to flip
Term
Gauge Pressure
Click to flip
Term
Vacuum Pressure
Click to flip
Term
Hydrostatic Equilibrium
Click to flip
The pressure exerted by a fluid at rest due to the weight of the fluid above it.
Pressure measured relative to atmospheric pressure; the pressure in an enclosed system minus atmospheric pressure.
Pressure that is below atmospheric pressure, indicating a partial vacuum.
The condition wherein the net force acting on a fluid element at rest is zero.
This section discusses the pressure distribution in a fluid at rest, focusing on how pressure varies in the z-direction while remaining constant in the x and y directions.
The section elaborates on pressure fields in a fluid at rest, indicating that under hydrostatic conditions, pressure only varies vertically (z-direction) due to gravity, while it remains constant across horizontal planes. It also explores concepts like gauge pressure, vacuum pressure, and presents various equations illustrating these principles.
This section explores the behavior of pressure in fluids at rest, specifically in a hydrostatic scenario. When a fluid is at rest, it experiences no shear stress, meaning that pressure is the only normal stress acting on control surfaces. The pressure is defined as a function of three coordinates, P(x, y, z), allowing for analysis in Cartesian coordinates.
According to Pascal's principle, pressure within a static fluid acts equally in all directions, leading to pressure only varying with respect to the vertical height (z-coordinate). In a horizontal plane (x-y plane), the pressure remains constant across the surface. When deriving the pressure components, the weight of the fluid column above a point in the fluid body must be considered alongside surface forces. The relationship between pressure and height is linearly proportional, which can be understood through the following equation:
where ρ is the fluid density and g represents the acceleration due to gravity.
The text also introduces the concepts of gauge pressure and vacuum pressure, explaining how these relate to atmospheric pressure measurements. Gauge pressure is the pressure above atmospheric pressure, while vacuum pressure refers to pressure below atmospheric conditions. This duality emphasizes the importance of establishing a datum when measuring pressure. The section concludes with examples and practical applications to reinforce these concepts.