Exam 1 Flashcards
What four quantities have we talked about that all have the same dimensions?
Energy, heat, work, torque
Of those four, what’s special about torque?
Torque is a vector quantity
Can gage pressure be negative? Why or why not?
yes, Gauge pressure is positive for pressures above atmospheric pressure and negative for pressures below it.
Can absolute pressure be negative? Why or why not
Absolute pressure can not be negative because it is referenced to zero so that its lowest
absolute pressure can be is 0 psi.
Convert [some number] in vacuum pressure to gage pressure
Vacuum range is the negative range of gauge pressure. -Vacuum pressure = gauge
pressure.
Convert [some number] in vacuum pressure to absolute pressure
Absolute pressure = Gage Pressure + Patm = -Vacuum Pressure + Patm
What’s momentum?
mass x velocity
How does force relate to momentum?
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.
What are the SI units of density?
The SI units of density are 𝑘𝑔/ 𝑚^3
What are the SI units of force?
kgm/ s^2
What’s a Newton
is the SI unit derived for a unit of force.
example of an object that weight about 1 N
an apple
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.
degrees x (2piradians/360 degress) = number of radians
SI units of momentum
kg m/ s
SI units of heat
1 Joule = 1 kgm^2 / s^2
symbol for specific gravity
S.G.
What’s viscosity
Viscocity is like the stickiness of a fluid, like friction. Causes energy loss.
SI units of shear force
kg m / s^2
What is specific weight
Specific weight is the weight per unit volume, 𝛾 = 𝜌𝑔.
SI units of shear stress
kg/ s^2 m = 1 Pascal
symbol for specific weight
gamma, 𝛾
What’s a joule in terms of kg, m, s
kg m^2/ s^2
density of water in SI
1000 kg/m^3
What’s atmospheric pressure in BG (British gravitational)
14.7 psi
whats the density of air in SI
1.2 kg/ m^3
atmospheric pressure is SI
101 kPa (kN/m^2)
what does psi stand for
pounds per square inch
about how much more dense is water than air
water is about 1000 times more dense than air
about how much less dense is air than water
air is about 1000 times less dense than water
In gage pressure, what is the pressure a distance D down into a vat of fluid of density rho
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
In absolute pressure, what is the pressure a distance D down into a vat of fluid of density
rho?
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.
If a tank has height H, what is the gage pressure a distance D up from the bottom of the pool
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)
If a tank has height H, what is the absolute pressure a distance D up from the bottom of
the pool?
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.
Write the equation that relates linear velocity to angular velocity and show how the
dimensions work out
𝑣 = 𝜔𝑟 [𝑚/𝑠] = [1/𝑠][𝑚] = [𝑚/𝑠]
What is another name for Conservation of Momentum in differential form?
Another name for Conservation of Momentum in differential form is Navier-Stokes
equation
What is another name for Conservation of Mass in differential form?
continuity equation
Write an equation to integrate [a function of r and theta] over a circle
∫0 to 2pi ∫0 to R 𝑓(𝑟, 𝜃)𝑟 𝑑𝑟𝑑𝜃
Write the del operator (nabla)
∇ = (𝜕/𝜕x)i +(𝜕/𝜕y)j +(𝜕/𝜕z)k
. Given V = a vector, find del dot V, V dot del, V dot del V, the Laplacian of V,
doc
Can you take the divergence of a scalar?
No
Show how to derive x = ½ at^2 + v0t + x0 starting from a = a and hold your answer up
to the camera.
𝑎 = 𝑎 𝑣 = ∫ 𝑎𝑑𝑡 = 𝑎𝑡 + 𝑣𝑜
𝑥 = ∫ 𝑣𝑑𝑡 =1/2𝑎𝑡^2 + 𝑣𝑜𝑡 + 𝑥o
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?
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.
Now double the area of the pool. How do the pressures at those two points change?
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
Find the normal vectors to [the sides of a triangle shown] and hold your answer up to the
camera.
examples in the doc
Can the del operator operate on a scalar?
The del operator can operate on a scalar. If you take the gradient of a scalar, it yields a
vector
Can the del operator operate on a vector?
The del operator can operate on a vector. If you take the gradient of a vector, it yields a
tensor.
What are the two ways to multiply vectors?
cross product and dot product
is the gradient a form of vector multiplication
no
Given a line on a graph with some identifying points, write the equation for that line
examples in the doc
What are the dimensions of area moment of inertia
m^4
𝐼𝑥 = ∫ 𝑦^2𝑑A
What are the dimensions of mass moment of inertia
kgm^2
𝐼𝑥 = ∫ 𝑦^2 𝜌 𝑑A
What is a pascal
A pascal is the SI unit derived for quantifying pressure.
Pa= N/m^2 = kg/ ms^2
what is specific gravity
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.
