6. Fluids

Question 1

What is the formula for density?

Answer 1

ρ = m / V

mass = kg 
V = m^3

Question 2

What is specific gravity? what is the density of water?

Answer 2

specific gravity is a substances density relative to water. The density of water is 1g/cm^3 or 1kg / L
1L = 1000cm^3

specific gravity = ρ / ρ H2O

Question 3

How can we calculate the force of gravity acting on a fluid?

Answer 3

Fg = w = mg

ρ = m / V

Weight of fluid (Fg) = ρ • V • g

Question 4

What is the formula for pressure? What is its units?

Answer 4

P = F / A

N / m^2 = pascals

1 atm = 100kPa = sea level

Question 5

What is hydrostatic gauge pressure? What does gauge mean? What is the formula?

Answer 5

hydrostatic gauge pressure is the pressure exerted on an object due to its weight. Gauge indicates the atmospheric pressure is not taken into account.

P = F / A = mg / A = ρVg / A = ρADg/A = …

P = ρ • D • g

Question 6

t or f, if we want to know the total pressure on an object we need to add P-total with P-gauge.

Answer 6

true, only if the object is exposed to the atmosphere.

also, if the object was not exposed to atmosphere but was exposed to some other pressure than its P-surface + p-gauge

Question 7

t or f, total pressure is proportional to depth and density

Answer 7

FALSE, gauge pressure is, as seen in the equation P = ρ • D • g.

since total pressure does not pass through a graphs origin (0,0), it is not proportional.

Question 8

t or f, pressure is a scalar

Answer 8

true

Question 9

When an object is floating, there is a disproportionate amount of fluid interacting with the bottom of the object then the top. Thus, the bottom part of the object feels an upwards force from the fluid known as the buoyant force. What is Archimedes principle? What is the equation?

Answer 9

Archimedes principle states that the buoyant force is equal to the weight of the fluid that is displaced by the object floating.

Fg = mg 
ρ = m / V

Fb = ρ-fluid • V-submerged • g

Question 10

t or f, for a floating object Fg = Fb = weight of object. What is the consequence?

Answer 10

true, otherwise it would sink or rise.

Fg = Fb
m(o)g = ρ(f) • V(sub) • g
m = ρ x V 

ρ(o) x V(o) = ρ(f) x V(sub)

Question 11

Based on Fg = Fb, we can re-write the derived formula as

V(sub) / V(o) = ρ(o) / ρ(f)

Answer 11

This means that the density ratio of two fluids is equal to the ratio of the amount of volume submerged that is necessary for an object to float.

Question 12

If an object has a lower density than the fluid it is in what happens? What if they are the same density?

Answer 12

If the object has a lower density, it will float.

if ρ-object = ρ-fluid, it will hover just below the surface if water in static equilibrium.

Question 13

If an object is fully submerged in a fluid, how do you find its apparent weight?

Answer 13

An object fully submerged will have a maximum buoyant force opposing its own weight. So the ‘apparent weight’ of the object will be W - Fb

apparent weight = mg - (ρ-fluid • Vsub • g)

Question 14

What is Pascals Law?

Answer 14

Pascals Law states that an applied pressure to a confined fluid will transmit that pressure change throughout the fluid without loss of energy.

In other words, in two different sections of a pipe

P1 = P2

F1 / A1 = F2/A2

Question 15

What is flow rate? What is its formula?

Answer 15

In hydrodynamics, a certain amount of fluid passes through some point in a pipe every minute (unit of time). this is flow rate.

f = Av

A = cross sectional area of the tube / pipe / etc. 
v = average speed of the fluid

Question 16

What is the formula for fluid continuity?

Answer 16

continuity explains that in one pipe, the flow rate is equal through out all sections of the pipe. Therefore,

A1 • v1 = A2 • v2

Question 17

Bernoulli’s equation is a statement showing the conservation of total mechanical energy of a fluid. Due to its nature, it applies only to ideal fluids. What four things must a fluid satisfy to be an ideal fluid?

Answer 17

1. Fluid is incompressible (constant pressure)
2. Viscosity is negligible (i.e. no friction)
3. Flow is laminar (smooth)
4. Flow rate is steady (f is constant)

Question 18

What is Bernoulli’s equation?

Answer 18

Recall conservation of total mechanical energy

KE1 + PE1 + W = KE2 + PE2

P1 + 1/2ρv1^2 + ρgy1 = P2 + 1/2ρv2^2 + ρgy2

W = pressure (P)

Question 19

When you poke a hole in a container, fluid spills out of that container via an efflux speed. What is Torricelli’s result?

Answer 19

Torricelli’s result explains that we can manipulate Bernoulli’s equation to find the efflux speed of the fluid. Since there is a hole, the fluid at each end is at 1 atm (P1 = P2). We can also assume that v1 is negligible since the area of the container is much greater than the hole.

after rearranging,

Ve = square-root(g2D)

D = the distance from the surface of the container to the hole

Question 20

If a container full of fluid is at rest and open to the atmosphere, how can we find the pressure at some depth (y) in the container? Hint: hydrostatic gauge pressure and Bernoulli’s equation

Answer 20

At rest, so velocity terms cancel out
P1 + ρgy1 = P2 + ρgy2

P2 = P1 + ρgy1 - ρgy2
P2 = P1 + ρg(y1 - y2) 

P2 = P1 + ρgD

Note that ρgD gives hydrostatic gauge pressure. Adding it to P1 (usually atmospheric P) gives total pressure.

Question 21

What is the Bernoulli effect (Venturi effect)? Hint: Height of fluid is equal.

Answer 21

In situations where the heights of a fluid are pretty similar, these terms go to zero.
P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2

We also know by the continuity equation, that in smaller cross-sectional areas, velocity must increase. By the above equation then, if velocity increases, pressure decreases.

This is the Bernoulli effect.

Question 22

What is tension, compression, and shear forces?

Answer 22

These are all kinds of forces that solids may feel.

tension = stretching force
compression = squeezing 
shear = bending

Question 23

What is stress, how is it different than pressure?

Answer 23

stress = F / A

same equation as pressure, but with stress the force can be applied in any direction (pressure, it must be perpendicular)

Question 24

What is strain? What is its formula?

Answer 24

Stress is pressure, strain is change. Strain refers to how much a solids shape changes under a stress force.

compression or tension strain = ΔL / original length

shear = distance of shear / original length

Question 25

What is Hooke’s Law of stress?

Answer 25

Stress causes strain and therefore they are proportional (as long as there is not so much stress to which an object becomes permanently deformed).

stress = modulus x strain

modulus = constant for a given material