Hydrostatics

Question 1

What does the area moment of inertia reflect

Answer 1

How the area of a cross section is distributed relative to a particular axis, a measure of how much resistance the cross section has to bending.

Question 2

What is the equation to work out area moment of inertia

Answer 2

X axis:
Ix = ∫ y^2 * dA

Y axis:
Iy = ∫ x^2 * dA

dA = change in area = b * dy ( or dx)

Question 3

Define centroid

Answer 3

The geometric centre of a cross section

Question 4

What is the parallel axis theorem

Answer 4

Ix = Ixc + Ad^2

The equation is used to obtain the moment of inertia for any parallel axis to the centroidal axises x or u

Ixc = Moment of inertia centroidal axis
(Equation found in formula booklet)

Question 5

What is the perpendicular axis theorem

Answer 5

Also known as the polar moment of inertia (J)

It represents the resistance of cross section to twisting about the reference axis (x&y)

J = Ix + Iy

Question 6

Equation for normal stress, when bending

Answer 6

σ = - My/I

M = bending moment
y = distance
I = second moment of inertia

Question 7

How do you find the centroid of a given area

Answer 7

If object is irregular split into regular shapes

x axis:
x 1A1 + x 2a2
————————
A1 + A2

Y axis = same as x just in terms of the y axis’s

x = centroid x coordinate of the shape

Question 8

How do you work out the maximum tensile and compressive stresses of a material

Answer 8

For a positive moment the top surface is under compression and the bottom is under tension. Use the distances from the centroid axis and calculate σ

Question 9

Define hydrostatic force

Answer 9

The upward force exerted by a fluid on an object which is submerged, also known as the buoyant force.

Question 10

Define centre of pressure

Answer 10

The singular point at which the total hydrostatic force acts (where all the pressure forces act).

Question 11

How do you calculate the centre of pressure

Answer 11

Ic
= ——— + yc
A*yc

Ic = moment of inertia
A = area of body
yc = vertical distance to centroid

Question 12

What do we assume when using Bernoulli’s Equation

Answer 12

• the points are along the same streamline
• the fluid is incompressible
• inviscid fluid (shear forces = 0)
• steady flow (flow doesn’t vary with time)

Question 13

Equations for dynamic and hydrostatic pressure

Answer 13

Dynamic:
1/2 ρ*v^2

Hydrostatic:
ρgh

Question 14

Define Bernoulli equation

Answer 14

P + 1/2*ρv^2 + ρgh = constant
Static pressure + dynamic pressure + hydrostatic pressure = constant

Question 15

What does Bernoulli’s equation state

Answer 15

That the sum of the pressure, kinetic and potential energy remain constant along a streamline

Question 16

Define a streamline

Answer 16

The path traced by a single particle within a fluid

Question 17

What is Bernoullis principle

Answer 17

An increase in velocity results in a decrease in pressure

Question 18

Define stagnation pressure

Answer 18

The static pressure at a stagnation point (v = 0) in a fluid

= P + 1/2*ρv^2

Question 19

Define flow rate

Answer 19

How much of a fluid passes through a cross-sectional area
Q = vA

v = flow velocity
A = cross-sectional area