Fluid Mechanics Flashcards
Science of fluid at rest is called
Fluid statics
Fluid pressure
F/ change in area
1 atm=
1.013 x 1^5 Pa
1 Torricelli’s (torr) =
133 Pa
Relative density
Is the ratio of density of a substance to the density of water at 4 C
Pressure due to fluid column
h x density x g
Gauge pressure =
Real pressure - atmospheric pressure
Pascal’s Law
States that on changing the fluid pressure at any point the change is transmitted to the entire liquid without being diminished in magnitude
Applications of pascals law
Hydraulic machines like hydraulic brakes,lift,etc.
Archimede’s Principle
States that the loss in weight of a submerged body is equal to the weight of liquid displaced by it
Mathematical form of Archimedes principle
V• =
V x [1 - (density of body /density of liquid)]
Laws of floatation
States that if:
1] density of body > density of liquid –> it’ll sink
2]density of body = density of liquid–>
It’ll float fully submerged..I.e..just below the liquid surface
3]density of body
It’ll float partially submerged such that
V x density of body = Vim x density of liquid
Continuity equation
Av = constant
Pressure energy =
pAl
Pressure energy per unit volume =
p
Kinetic energy=
(1/2) x m x v^2
Kinetic energy per unit volume =
(1/2) x density x v^2
Potential energy=
mgh
Potential energy per unit volume =
h x density x g
Bernoulli’s Theorem
States that for a streamlined motion of an ideal fluid the total energy is always constant throughout
Applications of Bernoulli’s Theorem
1] carburettor 2] paint gun 3]scent sprayer and atomiser 4] Magnus effect 5] Aerofoil 6] Bunsen burner, gas burner, oil stove actions 7] Torricelli's Theorem 8] venturimeter 9] pitot tube
Limitations of Bernoulli’s Theorem
1] it’s applicable only to streamlined motion and not steady or turbulent flow since in these cases the velocity and pressure fluctuates with time
2] it’s applicable only to ideal fluids
3] at rest the Bernoulli’s Theorem changes to
(p-p’) = (h’-h) x density x g
Torricelli’s law
States that efflux of water is same as that of a freely falling body under gravity
Mathematical form of Torricelli’s Law
v = (2gh) ^1/2
Volume of liquid coming out of an orfice
A x (2gh)^1/2
Time period of liquid coming out of an orfice
T = (14||/15) x (R^5/2)/a(2g)^1/2
Surface tension =
F/L
Consequence of surface tension
Is that pressure inside a soap bubble is greater than the atmospheric pressure outside
Excess pressure for a liquid/air drop
p = 2T/R
Excess pressure for a soap bubble
p = 4T/R
Increase in surface energy =
T x change in area
Relation between angle of constant and temperature
Angle of contact increases with increase in temperature
Relation between angle of contact and impurities
Angle of contact decrease with increase in impurities
Rise in capillary tube =
h = 2T/ ( r x density x g)
Rise in capillary if the tube is tilted by an angle @
l = h/cos@
where h is the rise in capillary when the tube is vertical
For insufficient height of tube
hR = h’R’
After connection of capillary tube
h = 2T /(r x density x g) - r/3
While flowing in a tube the velocity of liquid is
Maximum along tube’s axis
0 at tube’s walls
What kind of flow do liquids have and why?
Laminar flow due to viscosity
Poiseuille’s Formula
Vplume of liquid flowing per second =
(|| x density x R^4) / 8 n L
Where n-coefficient of viscosity
Stokes Law
Force of viscosity =
6 || n r v
Where
n - coefficient of viscosity
v - terminal velocity
Terminal velocity=
v = (2/9) x [r^2 x (density of body - density of liquid) x g] / n
Where n- coefficient of viscosity
Reynolds Number(Re)
It tells us about the nature of flow of fluid
Assumptions based on values of Reynolds number
Value. Flow
Re3000. Turbulent
2000
What will happen to pressure in the absence of intermolecular forces
Pressure will increase
Work =
T x change in area
