Week 9 Flashcards
When looking at objects relative to sea level, what is our reference pressure?
If we look at objects floating on the water surface, they experience a pressure p, which is equal to the local atmospheric pressure.
This pressure p is our reference pressure which we’ll treat as “0”.
What is the equation for pressure? How is the pressure distributed across the object?
p=ρgh
p: pressure
ρ: “rho” aka the DENSITY of water
g: gravitational acceleration = 9.81m/s^2
h: height of the water column above our object
The pressure is distributed over the surface of the object and is directed perpendicular to the object surface at all points.
Why isn’t area part of the pressure formula? What are the units of pressure?
As the area of our object gets bigger, the volume, and hence the weight of the water column also increases. The weight is distributed over a proportionally larger area, so the pressure remains unchanged.
The units of pressure is:
- force per unit area
- N/m^2
- Pascals
What is the expression for Q_out? What can you rearange the expression to (relate to pressure formula)? What is the pressure in the rearanged equation of? Where does it come from?
Q_out=A_nozzlesqrt(2g*h)
area of the nozzle times the square root of 2 times the gravity acceleration times height
Q_out=A_nozzlesqrt((2pressure)/ρ)
area of the nozzle times the aquare root of (2 times the pressure) divided by the density
- THE PRESSURE RHERE IS THAT IMMEDIATELY BEFORE THE NOZZLE OUTLET.
- The pressure comes from the height of the water column in the tank
Why does increasing the diameter of the tank not affect the flowrate?
as d gets bigger, the weight of the water column in the tank gets bigger, but it’s also distributed over a larger cross-sectional area, so the pressure doesn’t change and therefore, flowrate stays the same!
How do we get the velocity of the low out of the tank? (from the Q_out Equation)?
Q_out=A_nozzlesqrt((2pressure)/ρ)
Flowrate out divided by the are of the nozzle gives us velocity, so move A_nozzle to the other side:
v_out=sqrt((2*pressure)/ρ)
how do we get pressure in terms of velocity?
We can take our v_out formula and rearange for p:
p=(ρ(v_out)^2)/2
Flow travels from high pressure to low pressure. The velocity out is due to the fact that the pressure in the tank is higher than the pressure outside the tank!
Ex/ Blowing a balloon works because your lungs create a pressure greater than the pressure inside the balloon. Air flows from high to low pressure, hence why the balloon blows up!
If you had 2 tanks, one with a bigger high and one with a smaller height, What happens when you open flow between them?
The water from the higher tank flows into the lower tank until they r even h value.
In terms of the pressure from velocity equation, Normally:
p=(ρ(v_out)^2)/2
but, if the pressure outside the nozzle isn’t 0 (atmospheric pressure), then we replace p with p1-p2:
p1-p2=(ρ(v_out)^2)2
When the valve is initially open, the p1-p2 difference exists, causing fluid to flow from high pressure to low pressure. Eventually, the equalize and the difference is 0, meaning there’s no longer anything to drive flow and that’s why it eventually stops.
How is rainfall usually measured? What does it mean? Do wider containers get more height and stuff?
Usually measured in units of height per time, such as “10mm of rain overnight”.
This basically means that there is a volume flowrate of rain per unit area.
If we put a wider container and a skinnier container, they’ll both have the same height of water, but different volumes!
For a spreadsheet, how would you compute Q_in for a situation where we’re catching rainfall from a roof of a simple house?
Equation: = “rainfall of the particular day” / 1000mm (to convert to m) * catchment area
For a spreadsheet, how would you compute the Volume for a situation where we’re catching rainfall from a roof of a simple house?
For the first day, equation:
= “initial volume” + “Q_in for the specific day”
For the rest of the days, equation:
= “volume in tank at end of previous day” + “Q_in for the specific day”
Whats an easy way to insert a chart with a lot of data?
Select all the data, insert chart, click on any bar of data you don’t want and press delete!
