Princeton Ch 8 - Fluids

Question 1

Fluids.

Answer 1

Substances that can flow (ie. gases and liquids).

Question 2

Difference between liquid and gas.

Answer 2

The molecules in a liquid are able to move around a little more freely than in those of a solid, which molecules typically only vibrate. By contrast, molecules in a gas are not constrained and fly around in a chaotic swarm, with hardly any interaction.

Question 3

Density.

Answer 3

The amount of mass contained in a unit of volume.

ρ = m/V [kg/m^3]

Question 4

The density of water.

Answer 4

1000 kg/m^3
1 g/cm^3
1gkg/L, where L stands for liter (a liter is 1000cm3)

Question 5

Specific gravity.

Answer 5

How dense something is compared to water.

Specific gravity = density of substance/density of water

Question 6

True or false. For solids, liquids, and gases, density doesn’t change much with changes in pressure or temperature.

Answer 6

Solids and liquids behave the same way under most conditions.

However, the density of gas changes markedly with pressure and temperature. PV =nRT; ρ(gas) = mV = mP/nRT

Question 7

How does one find the force of gravity acting on a fluid?

Answer 7

ρ = m/V –> m = ρV –> F(grav) = mg = ρVg

Question 8

If we place an object in a fluid, the fluid exerts a contact force on the object. If we look at how that force is distributed over any small area of the object’s surface, we have the concept of pressure. What is P?

Answer 8

P = Force/Area

Question 9

Hydrostatic gauge pressure.

Answer 9

The weight of a fluid above a submerged object produces a force that pushes down on a point. This is called hydrostatic because the object is at rest, and gauge because we don’t take the pressure into the atmosphere into account. If we did we/d have to add it.

P(gauge) = ρ(fluid)gD
D = depth of the point

Question 10

If you have an object submeged in water, how do you find the total pressure?

Answer 10

P(total) = P(at surface) + Pguage

P(at the surface) = atmospheric pressure or the layer of gas above the surface of the liquid.

Question 11

True or false. Density doesn’t increase with depth for liquids.

Answer 11

True. The density of a liquid should remain the same.

Question 12

True or false. Hydrostatic gauge pressure and the TOTAL pressure is proportional to both the depth and the density of the fluid.

Answer 12

False. Guage pressure = ρ(fluid)gD, is proportional to both depth and density of the fluid.

Total pressure is NOT proportional to either quantity of P(on the surface) isn’t zero.

Question 13

1 Pascal =?

Answer 13

1N/m^2

Question 14

If you have a hourglass beaker filled with water, and a regular beaker filled with water, what is the pressure at the bottom right corner?

Answer 14

The pressures are the same if the fluid density and depth are the same. P(guage) = ρfluidgD, regardless of the shape of the container in which the fluid is held. The pressure is the same everywhere along a horizontal dashed line.

Question 15

Archimedes principle.

Answer 15

The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.

F(buoy) = ρ(fluid)V(sub)g

Question 16

Buoyant force.

Answer 16

The net upward fluid force.

F(buoy) = ρ(fluid)V(sub)g

Question 17

For a floating object, __ = __. This is a floating object in equilibrium on the surface.

Answer 17

W(object) = F(buoy)

Vsub/V = ρ(object)/ρ(fluid)

Question 18

If ρ(object) < ρ fluid, then the object will ___.

Answer 18

The object will float and the fraction of its olume that’s submerged is the same a the ratio of its density to the fluid’s density.

Question 19

If an object’s density is 3/4 the density of the fluid, then __ of the object will be submerged.

Answer 19

3/4

Vsub/V = ρ(object)/ρ(fluid)

Question 20

If an object is denser than the fluid, then the object will ___.

Answer 20

The object will sink because the object’s weight is greater than the buoyant force.

Question 21

For an object that is completely submerged in water, the weight of the object is still the same.

Answer 21

True. The actual weight of the object is still w=ρVg. BUT, the object’s apparent weight is less due to the buoyant force pushing the object upwards.

w(obj)/F(buoy) = ρVg/ρ(fluid)Vg = ρobject/ρfluid

If the fluid was water, note that the ratio of the object weight to the buoyant force is equal to the specific gravity of the object.

Question 22

A glass sphere has a specific gravity of 2.5. How do you find the density of the glass sphere?

Answer 22

ρ(sphere ) = 2.5*(1000 kg/3^3)

Question 23

Pascal’s law on fluid pressure.

Answer 23

If you squeeze a container of fluid, the fluid will transmit your squeeze perfectly throughout the container.

Question 24

For a simple hydraulic jack consisting of two pistons above two cylindrical vessels of fluid, what can we say about force, area, and distance, if we push down on one piston?

Answer 24

F1/A1 = F2/A2 –> F2 = A2F1/A1 –> notice the greater output Force (F2); this is what makes hydraulic jacks useful.

But the volumes have to be the same. A1d1 = A2d2.

So ultimately,
F2d2 = (A2F1/A1)(A1d1)/A2 = F1d1; work you do pushing the left piston equals the work done on the right.

Question 25

In a simple hydraulic system, let’s say A2 is 5 times bigger than A1. What does this mean regarding the any applied force and the distance?

Answer 25

The increase in F is the same as the decrease in d. If A2 is 5 times larger than A1, then F2 will be 5 times greater than F1, but d2 will only be 1/5 of d1.

Question 26

Formula for surface tension.

Answer 26

F(surface tension) = 2γL

γ = coefficient of surface tension. 
2L = there are two surfaces in which this force acts. The force acts along a line, L.

Question 27

Flow rate.

Answer 27

The volume of fluid moving through a particular cross sectional area per unit of time.

f = Av = πr²*(v)

Question 28

Difference between flor rate and flow speed.

Answer 28

Flow rate tells us how MUCH fluid flows per unit time; speed tells us how FAST the fluid moves.
Ex. The hose ejects 4L of water/s versus the water leaves the hose at a speed of 4m/s.

Question 29

If a pipe carrying an incompressible liquid, then the flow rate must be same everywhere along the pipe. Give the continuity equation for liquids between point1 and point 2.

Answer 29

A1v1 = A2v2

Question 30

What can A1v1 = A2v2 tell us?

Answer 30

When the tube narrows, the flow speed with the increase, and if the tube widens, the flow speed with decrease. Note that flow speed is inversely proportional to the cross-sectional area. v α 1/A

Question 31

Bernoulli’s equation only applies to ideal fluids. Define what this is.

Answer 31

1) Fluid is incompressible.
2) Has negligible viscosity ( the force of cohesion between molecules in a fluid - fluid friction)
3) Flow is laminar - the flow is in a “streamline”
4) Flow rate is steady. “f” = Av is constant.

Question 32

Bernoulli’s equation:

Answer 32

P1 + 1/2ρv(1)² +ρgy1 = P2 + 1/2ρv(2)² +ρgy2

P = total pressure along that point; not guage
P1 - Patm (if 2 was exposed to air) = Pguage at 1

Question 33

Any fluid exposed to the atmosphere with Bernoulli equations is what pressure?

Answer 33

Atmospheric pressure.

1 atm = 101.3kPa

Question 34

At any two ponits of equal height (y1=y2), faster fluid flow means (lower/higher) pressure.

Answer 34

At any two points of equal height (y1=y2), faster fluid flow means LOWER pressure. P + 1/2ρv² = constant

For a syringe needle, the needle is smaller, so v is faster than in the plunger. faster fluid means LOWER pressure.

Question 35

Torricelli’s result.

Answer 35

ρgy1 = 1/2ρv(2)² +ρgy2; 
P1 = P2 = atm; v1 = 0 because A1>>>>A2

v(2) = √(2gD)
For a large tank exposed to atmosphere and then a small hole poked in the bottom.

Question 36

Bernoulli (Venturi) effect.

Answer 36

The pressure is lower where the flow speed is greater, if y1 = y2.

Question 37

Poiseulle’s law (may not have to remember)

Answer 37

ΔP/L = 8nf/(πr^4)

P = pressure gradient across tubing
n = viscosity coefficient
f = flow rate
r = radius of pipe
L = length of tubing

Doubling the diameter of a catheter increases the flow rate by 16 fold (r4). The larger the IV catheter the greater the flow.

Increasing viscosity decreases flow through a catheter.

Question 38

A pipe of constant cross sectional A carries water at a constant flow from the hot water tank in the basement oup to the second floor. What can you say about the speed and pressure at which the water arrive and leaves the water tank.

Answer 38

The water pressure at the second floor must be LOWER than the water pressure at the tank. Since the flow rate and A is constant, the flow speed will be constant. f = Av = constant.

P1 +ρgy1 = P2 +ρgy2