Unit 2: Hydrostatics

Question 1

What are the most common units of pressure?

Answer 1

Pa = N/m2
kPa = 10^3 Pa
MPa = 10^6 Pa

bar = 10^5 Pa

atm = 101325 Pa = 760 mm Hg

Question 2

What is absolute-, atmospheric-, gage- and vacuum pressure?

Answer 2

Absolute pressure: The actual pressure measured relative to absolute 0 pressure
Atmospheric pressure: the pressure of the atmosphere.

Gage/ Relative pressure: The difference between the absolute pressure and the atmospheric pressure
Vacuum pressure: pressures below atmospheric pressure.

Pgage = Pabs-Patm
Pvacuum = Patm-Pabs

Vacuum pressure + gage pressure = 0

Question 3

What is always true about the pressure at a point in a fluid at rest?

Answer 3

The pressure is isotropic:
The pressure at any point in a static fluid acts with the same magnitude in all directions

Question 4

What is Stevin’s law

Answer 4

The pressure at any point within a fluid at rest is only proportional to the depth of that point

∂P/∂x=0, ∂P/∂y = 0, ∂P/∂z = -ρg = -γ

Question 5

How does a manometer work?

Answer 5

A manometer uses a fluid column to measure the pressure differene
∆z = ∆P/ρg
∆P = ρgh
You can figure out the pressure by measuring the difference in elevation of the fluid.

Question 6

How can you find the resultant hydrostatic force acting on a submerged plane surface

Answer 6

FResultant is obtained by integrating the force PdA over the entire plane surface (A)

Question 7

What is special about the centroid of an submerged object?

Answer 7

The vertical distance of the centroid from the free surface of the liquid can be used to calculate the resultant hydrostatic force.

FR = PGA = γhGA

This removes the need to integrate over the area, and removes the need to know the shape of the object.

Question 8

Where is the resultant hydrostatic force applied?

Answer 8

At the center of pressure (CP)
Which is located a little below G

Question 9

What componetns do you need to find yCP?

Answer 9

IxG: second moment of area
yG: y-coordinate of the centroid
A: Area of the submerged surface

yCP = IxG/yGA + yG

Question 10

What is true about xCP for surfaces with areas that have symmetry about the X-axis

Answer 10

xCP = xG

Question 11

How do you find FH?

Curved surface

Answer 11

Create a vertical projection of the curved surface

FH = γhG-projA

Question 12

How do you find FV?

Curved surface

Answer 12

Calculate the weight of the liquid volume between the curved surface (AB) and the free surface

FV = γV

Question 13

How do you find FR?

Curved surface

Answer 13

Calculate the norm of the components of the resultant force vector

FR = sqrt(FV^2 + FH^2)

Question 14

How do you find the angle of application?

Answer 14

The angle α FR makes with the horizontal plane can be calculated through:

tan(α) = FV/FH