Fluid Mechanics: Density and Pressure
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1
relative density
density of substance/density of water at 4°c
2
density of mixture what is the condition of harmonic mean and what is the condition for arithmetic mean
p1v1+p2v2/(v1+v2) harmonic mean (m1=m2) p=2p1p2/(p1+p2) arithmetic mean (v1=v2) p=p1+p2/2
3
what makes the pressure difference with depth inside a fluid
weight of fluid
4
unit, dimension of pressure
N/m^2 ML^-1T^-2
5
variation of pressure with depth also when accelerating upwards, downward
P2-P1=hpg , P2-P1=hp(g+a), P2-P1=hp(g-a)
6
absolute pressure and gauge pressure
P=Pa+hpg(absolute pressure). P-Pa=hpg(gauge pressure)
7
average pressure on side walls with liquid level h
P=hpg/2
8
mercury barometer is used to calculate? also how many pascal is 1 atm also equation to calculate it also how many cm Hg is risen at sea level
measure atmospheric pressure 1atm= 1.013*10^5Pa,hpg,76cm ofHg
9
1 torr equal to how many Pa and how many mmHg
133Pa,1mmHg
10
1 bar how many Pa
10^5Pa
11
1atm how many torr
760 torr
12
height and pressure of water in inclined pipe of length l
h=lsin(theta),P=Pa+/pgsin(theta)
13
open tube manometer equation which liquid should be used for large pressure difference and small pressure difference
P=Pa+hpg use high density liquid for large pressure difference use low density liquid for low pressure difference
14
pascal law equation also what is the equation of mechanical advantage here (2) represent the output we get
F1/A1=F2/A2 , A2/A1
15
buoyant force
Fb=v.sigma.g here sigma is density of fluid and v is volume of displaced liquid
16
wapp=?
Wapp=Vpg(1-(Sigma/p))
17
law of floating for (floating)
W=Vpg ,Fb=Vin.sigma.g Vin/V=p/sigma Vout/V=1-p/sigma
18
p<sigma,p=sigma,p>sigma
Vin<V,Vin=V,Vin=V
19
when the body is completely submerged accelerates(upward,downward,freefall)
Fb(upwards)=sigma.V.(g+a), Fb(downwards)=sigma.V.(g-a) freefall Fb=0
20
equation of continuity
Av =constant A1V1=A2V2
21
bernoulli principle
P+1/2pv^2+pgh=constant, P/pg +v^2/2g +h =new constant P/pg= pressure head h=gravitational head v^2/2g=velocity head (P+pgh)=static pressure 1/2pv^2 =dynamic pressure
22
torricelli's theorem (vessel is open to atmosphere ), general case y1 is from bottom to hole y2 is height from bottom to the height of liquid
v=√2gh, Pa+1/2pv^2 +pgy1=Ppgy2 (h=y2-y1) v1=√(2gh+(2(P-Pa)/p))
23
Maximum range of Efflux,time of flight at which height is range maximum and what is the maximum range at that point
R=2√(h(H-h),T=√(2(H-h)) ,height is H/2 where range is maximum range at that point is H
24
time required for level of liquid to drop from H1 to H2 (here A is area of the top of the vessel and a is the area of the hole ) also what the time empty the vessel
t=A/a(√(2) *(√H1-√H2), t=A/a√(2h)
25
venturimeter(rate of flow Q) two equations
Q=A1A2√(2gh/(A1^2-A2^2) Q=A1A2√(2(P1-P2)/p(A1^2-A2^2) here P1-P2=hpg
26
blowing of roof by wind storm equation of pressure and force here V is the speed
∆P=p/2(Vout^2-Vin^2),F=(pA/2)*(Vout^2-Vin^2
27
Newton's formula for viscous force
F=-eta.A.dv/dx here -ve sign show the direction of force
28
stress is proportional to what ? also write equation
stress proportional to rate of change of strain (strainrate), F/A=eta.dV/l or F/A proportional to ∆x/l∆t
29
viscous fluid flow rate
Q=πPR^4/(8.eta.l)
30
stokes law
F=6π.eta.rv
31
terminal velocity
v=2/9(r^2/eta)*(p-sigma)g if is positive the. moving downward if negative moving upwards
32
surface tension
force/length
33
relation b/w surface energy and surface tension S is surface energy of liquid per unit area
S=F/2l
34
work done in forming a drop
W=S*4πr^2
35
work done in forming a bubble
W=2*S*4πr^2
36
Sla-liquid-air interfacial tension Ssa-solid-air interfacial tension Ssl-solid-liquid interfacial tension what their relationship at equilibrium what happenes when Ssl>Sla and what happens when Ssl<Sla
Sla cos(theta)+Ssl=Ssa , Ssl>Sla angle is obtuse example water interface(cohesive force is greater),Ssl<Sla angle is acute example plastic interface(adhesive force is greater)
37
pressure difference in plane surface, concave surface,convex surface
∆P=0(Pv=PL) ,Pv>PL(∆P=2S/R),Pv<PL(∆P=2S/R)
38
drops and Bubbles excess pressure
excess pressure inside a liquid drop(∆P=2S/R), inside soap bubble (∆P=4S/R), excess pressure inside an air bubble inside a liquid (∆P=2S/R)
39
bubble at depth h below the free surface of liquid of density p then pressure inside is given by
Pin=Pa+hpg+2S/R
40
bubble formation (formation of double bubble)
rcommon=r1r2/(r2-r1)
41
formation of single bubble from two bubbles of radio a and b under isothermal condition
r^2=a^2+b^2
42
ascent formula r is the radius of tube R is radius of curvature of liquid meniscus
h=2Scos(theta)/pgr h=2S/Rpg
43
rise of liquid in a capillary tube of insufficient height
hR=2S/pg =constant hR=h'R' here h'<h and R'>R R'=hR/h'
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