Exam 1

Question 1

What four quantities have we talked about that all have the same dimensions?

Answer 1

Energy, heat, work, torque

Question 2

Of those four, what’s special about torque?

Answer 2

Torque is a vector quantity

Question 3

Can gage pressure be negative? Why or why not?

Answer 3

yes, Gauge pressure is positive for pressures above atmospheric pressure and negative for pressures below it.

Question 4

Can absolute pressure be negative? Why or why not

Answer 4

Absolute pressure can not be negative because it is referenced to zero so that its lowest
absolute pressure can be is 0 psi.

Question 5

Convert [some number] in vacuum pressure to gage pressure

Answer 5

Vacuum range is the negative range of gauge pressure. -Vacuum pressure = gauge
pressure.

Question 6

Convert [some number] in vacuum pressure to absolute pressure

Answer 6

Absolute pressure = Gage Pressure + Patm = -Vacuum Pressure + Patm

Question 7

What’s momentum?

Answer 7

mass x velocity

Question 8

How does force relate to momentum?

Answer 8

Force relates to momentum through Newton’s second law of motion in terms of
momentum. The net external force equals the change in momentum of a system divided
by the time over which it changes.

F=Δp/Δt.

Question 9

What are the SI units of density?

Answer 9

The SI units of density are 𝑘𝑔/ 𝑚^3

Question 10

What are the SI units of force?

Answer 10

kgm/ s^2

Question 11

What’s a Newton

Answer 11

is the SI unit derived for a unit of force.

Question 12

example of an object that weight about 1 N

Answer 12

an apple

Question 13

Write an equation that relates the number of degrees in a circle to the number of radians
in a circle and show how the dimensions work out.

Answer 13

degrees x (2piradians/360 degress) = number of radians

Question 14

SI units of momentum

Answer 14

kg m/ s

Question 15

SI units of heat

Answer 15

1 Joule = 1 kgm^2 / s^2

Question 16

symbol for specific gravity

Answer 16

S.G.

Question 17

What’s viscosity

Answer 17

Viscocity is like the stickiness of a fluid, like friction. Causes energy loss.

Question 18

SI units of shear force

Answer 18

kg m / s^2

Question 19

What is specific weight

Answer 19

Specific weight is the weight per unit volume, 𝛾 = 𝜌𝑔.

Question 20

SI units of shear stress

Answer 20

kg/ s^2 m = 1 Pascal

Question 21

symbol for specific weight

Answer 21

gamma, 𝛾

Question 22

What’s a joule in terms of kg, m, s

Answer 22

kg m^2/ s^2

Question 23

density of water in SI

Answer 23

1000 kg/m^3

Question 24

What’s atmospheric pressure in BG (British gravitational)

Answer 24

14.7 psi

Question 25

whats the density of air in SI

Answer 25

1.2 kg/ m^3

Question 26

atmospheric pressure is SI

Answer 26

101 kPa (kN/m^2)

Question 27

what does psi stand for

Answer 27

pounds per square inch

Question 28

about how much more dense is water than air

Answer 28

water is about 1000 times more dense than air

Question 29

about how much less dense is air than water

Answer 29

air is about 1000 times less dense than water

Question 30

In gage pressure, what is the pressure a distance D down into a vat of fluid of density rho

Answer 30

Assuming that positive z is downward and the top is z = 0, the pressure at a distance D down into a vat fluid of density ρ, in gage pressure, is 𝑃 = 𝜌𝑔𝐷. P = rho g D

Question 31

In absolute pressure, what is the pressure a distance D down into a vat of fluid of density rho?

Answer 31

Assuming that positive z is downward and the top is z = 0, the pressure at a distance D down into a vat fluid of density ρ, in gage pressure, is 𝑃 = 𝜌𝑔𝐷 + 𝑃𝑎𝑡𝑚.

Question 32

If a tank has height H, what is the gage pressure a distance D up from the bottom of the pool

Answer 32

If a tank has height H, the gage pressure a distance D up from the bottom of the pool (z=0 at bottom) is 𝑃 = 𝜌𝑔(𝐻 − 𝐷)

Question 33

If a tank has height H, what is the absolute pressure a distance D up from the bottom of the pool?

Answer 33

If a tank has height H, the absolute pressure a distance D up from the bottom of the pool (z=0 at bottom) is 𝑃 = 𝜌𝑔(𝐻 − 𝐷) + 𝑃𝑎𝑡𝑚.

Question 34

Write the equation that relates linear velocity to angular velocity and show how the dimensions work out

Answer 34

``` 𝑣 = 𝜔𝑟 [𝑚/𝑠] = [1/𝑠][𝑚] = [𝑚/𝑠] ```

Question 35

What is another name for Conservation of Momentum in differential form?

Answer 35

Another name for Conservation of Momentum in differential form is Navier-Stokes equation

Question 36

What is another name for Conservation of Mass in differential form?

Answer 36

continuity equation

Question 37

Write an equation to integrate [a function of r and theta] over a circle

Answer 37

∫0 to 2pi ∫0 to R 𝑓(𝑟, 𝜃)𝑟 𝑑𝑟𝑑𝜃

Question 38

Write the del operator (nabla)

Answer 38

∇ = (𝜕/𝜕x)i +(𝜕/𝜕y)j +(𝜕/𝜕z)k

Question 39

. Given V = a vector, find del dot V, V dot del, V dot del V, the Laplacian of V,

Answer 39

doc

Question 40

Can you take the divergence of a scalar?

Answer 40

No

Question 41

Show how to derive x = ½ at^2 + v0t + x0 starting from a = a and hold your answer up to the camera.

Answer 41

``` 𝑎 = 𝑎 𝑣 = ∫ 𝑎𝑑𝑡 = 𝑎𝑡 + 𝑣𝑜 ``` 𝑥 = ∫ 𝑣𝑑𝑡 =1/2𝑎𝑡^2 + 𝑣𝑜𝑡 + 𝑥o

Question 42

Consider the pressure at a point 1 foot down into the water in the shallow end of a swimming pool. How much bigger or smaller is it than the pressure at a point 1 foot down into the water in the deep end of the pool?

Answer 42

The pressure is the same for the pressure at a point 1 foot down into the water in the deep end of the pool and the pressure at a point 1 foot down at the shallow end of the pool because pressure only varies with depth, it does not depend on width or length.

Question 43

Now double the area of the pool. How do the pressures at those two points change?

Answer 43

Doubling the area of the pool does not change the pressure at those two points because pressure only varies with depth, it does not depend on width or length

Question 44

Find the normal vectors to [the sides of a triangle shown] and hold your answer up to the camera.

Answer 44

examples in the doc

Question 45

Can the del operator operate on a scalar?

Answer 45

The del operator can operate on a scalar. If you take the gradient of a scalar, it yields a vector

Question 46

Can the del operator operate on a vector?

Answer 46

The del operator can operate on a vector. If you take the gradient of a vector, it yields a tensor.

Question 47

What are the two ways to multiply vectors?

Answer 47

cross product and dot product

Question 48

is the gradient a form of vector multiplication

Answer 48

no

Question 49

Given a line on a graph with some identifying points, write the equation for that line

Answer 49

examples in the doc

Question 50

What are the dimensions of area moment of inertia

Answer 50

m^4 𝐼𝑥 = ∫ 𝑦^2𝑑A

Question 51

What are the dimensions of mass moment of inertia

Answer 51

kgm^2 | 𝐼𝑥 = ∫ 𝑦^2 𝜌 𝑑A

Question 52

What is a pascal

Answer 52

A pascal is the SI unit derived for quantifying pressure. | Pa= N/m^2 = kg/ ms^2

Question 53

what is specific gravity

Answer 53

the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.