Lecture 5-6 Flashcards
What is Fb representitive of?
Buoyancy force
Fb =
Buoyant force =
ρf g (s+h) A - ρf g s A
density of the fluid x gravity x (depth + thickness) x area - density of ….. x …. x depth x …. x …..
Resultant equation of Fb =
ρf g v
density of fluid x gravity x volume
Magnitude of buoyant force must be equal to
weight of displaced fluid volume
An immersed neutrally buoyant body is stable if
the center of the gravity is directly below the center of buoyancy of the body
What it is called when the center of gravity and center of buoyancy is on the same point?
neutrally stable
What is it called when the center of gravity is above the center of buoyancy force?
Unstable
When an unstable body is submered in a fluid, what occurs?
It rotates using a restoring moment to get the center of gravity to be below the center of buoyant force
Condition for floatation: buoyancy force =
weight of body
Fb = W
How to use specific gravity of a material to work out whether a body will float or sink in a fluid?
Look at whether the specific gravity of the body is larger or smaller compared to the specific gravity of the fluid
The metacenter is
a line linking the new center of buoyant force to the geometrical central line that cuts through the body
When the metacenter point is above the center of gravity the body is said to be
stable
When the metacenter point is below the center of gravity the body is said to be
unstable
there is an overturning moment
A system is defined as
a collection of mass
m sys = constant is called
mass conserved
Energy conservation: change in E sys =
W net in + Q net in
When analysing a control volume, you must account for
in & out flows
(m cv) =
ρ (V cv)
density X volume of control volume
Q =
A1 v1
Q in fluid dynamics represents
volume flow rate
Volume flow rate is directly represented with the equation ……. and can be simplified further to …..
ΔV / Δt = A1 v1
change in volume / change in time = area X velocity
Mass flowrate is resolved by using the volume flow rate equation by….
m = ρ Q = ρ A v
density of fluid X volume flow rate = density of fluid X area flow through X velocity
Equation that links the two inlets into a control volume and the rate of change of fluid mass in CV;
dmCV / dt = Σm in - Σm out
change in fluid mass in CV / change in time = flow rate of mass in - flow rate of mqws out
In a steady flow system what can we assume about the inlet and outlet of the CV? Mass flow rate equation becomes?
that both flow rates of mass into and out of the system are equal so
m in - m out = 0
m in = m out
Σm1 = Σm2 can be expanded to
Σ (ρ1 A1 v1) = Σ (ρ2 A2 v2)
For incompressible flows —— is assumed as constant throughout
ρ - density of the fluid
For incompressible flows how can we write the steady flow equation?
Σ (A1 v1) = Σ (A2 v2)
