Lecture 4 Physics 2018/2019 • Hydrostatic pressure Hydrostatic pressure – p = ρgh 1 atm=760 mmHg (torr) SI 1 atm= 101 325 Pa
푝푉 = 푛푅푇
1 푚표푙 8,314퐽푚표푙−1퐾−1273,15퐾 푝 = 0,02241푚3
푝 = 101 325 푃푎 • Archimedes’ principle – buoyant force
Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes of Syracuse FB=h2ρgA-h1ρgA=(h2-h1)A ρg=V ρg=mg Density, pycnometry ρ = m/V [ρ] = 1 kg/m3
Vp – known or measured with a known liquid
solid 1. weight of solid material 2. volume of solid material (weight of empty pycnometer, pycnometer+ solid, pycnometer+ water-pycnometer+water+ solid)
Mohr-Westphal balances Bouyancy • Pascals law
When additional pressure exerted to an confined liquid, the pressure is transmitted equally to all parts of the liquid.
- reason incompressibility of liquids - consequence hydraulic press (hydraulic jack) 푝1 = 푝2
퐹1 퐹2 = 푆1 푆2
푆2 퐹2 = 퐹1 푆1 hydraulic ratio
m1=90 kg m2=5000 kg S1=? 2 S2=π r2 F= mg r1=0.134 m d1=0.268 m • Hydrodynamics Ideal liquid – incompressible, no viscosity, real liquids – little compressible, viscous
Ideal liquids 3 -1 -1 Volume-, mass- rate of flow – QV [m s ], Qm [kgs ]
incompressibility => Sv = constant ρSv=mv = constant V = Svt m=ρSvt Kinetic energy
Potential energy
Pressure energy Steady state – non-viscous, incompressible dE = 0 => E=constant Bernoulli’s equation 1 휌푣2푑푉 + 휌𝑔ℎ푑푉 + 푝푑푉 = 푐표푛푠푡푎푛푡 2
1 2 휌푣 + 휌𝑔ℎ + 푝 = 푐표푛푠푡푎푛푡 Daniel Bernoulli 2 (1700-1782) consequencies • Torricelli’s theorem
Evangelista Torricelli (1608-1647)
h1
v2 Viscosity- resistance to flow material constant, decreases with increasing temperature [ η] =1 Pa s dynamic viscosity
푑푣푥 퐹 = 푆휂 = 푆휏 푑푦 τ – shear stress kinematic viscosity 휂 휐 = [ν]=1 m2s-1 휚 Fluidity 1 휑 = [ϕ]= 1Pa-1s-1 휂 Real liquids - Stokes’ law (falling-sphere viscosimeter) Laminar flow, uniform spherical, smooth particles
drag force gravity bouyancy in equilibrium • Settling velocity in gravitational force
sedimentation of emulsions – stability of emulsions
2 2 2 • Settling velocity in centrifuge af=ω R=4π f R • Laminar and turbulent flow
Reynold´s number – ratio of inertial and viscous forces laminar flow Re<2000 휚푣푙 푣푙 푅푒 = = turbulent flow Re>2000 휂 휐 (fully RE> 4000) Korotkoff sounds Real liquid – little -compressible fluid with viscous stress forces, laminar flow flow volume rate resistance to flow
Poiseuille’s law
Qv
Qv A 16 % decrease in radius will halve the volume flow rate! • 16% occlusion –> r2=0.84r1
Δp1=Δp2=120 mmHg 3 Qv1=100 cm /min
Qv2=? Thermal physics Temperature – T (t) – Intrinsic property – independent on the amount of the material
temperarure = average kinetic energy of molecules
[T] = 1 K = 1oC T = t + 273.15 oC Measurement of temperature properties of materials varying with temperature • volume
• electrical properties
• pressure (gauges thermometers)
• IR radiation…. • Temperature scales Kelvin – [T] = 1 K Celsius – [t] = 1 oC
0 oC = 273.15 K 100 oC = 373.15 K water freezing-boiling
o T1 K = (t1 + 273.15 ) C o T2 K = (t2 + 273.15 ) C o (T1 - T2) K = (t2 - t2 ) C
T=0K => p=0, V=0 impossible to reach • Thermal expansion of materials α – linear (area, volume ) thermal expanson coefficient [α]=K-1
• Density variation with temperature
Density decreases with increasing temperature! • Anomaly of water density 0
Hydrostatic pressure 푝ℎ푦푑푟 = ℎ휚𝑔
Archimedes’ principle 퐹 = 푉푆(휚푠 − 휚푙 )𝑔 퐹 퐹 Pascal’s law- hydraulic press 1 = 2 푆1 푆2 푑푣 휂 Viscosity 퐹 = 휂 푆 푥 휐 = 푑푦 휚
Hydrodynamics 푄푣 = 푆푣 푄푚 = 푆푣휚 1 2 Bernoulli’s equation 2 휌푣 + 휌𝑔ℎ + 푝 = 푐표푛푠푡푎푛푡 Torricelli’s theorem 푣 = 2𝑔ℎ
Stokes law 퐹푑 = 6휋휂푟푣 2 푟2 휚 −휚 𝑔 2 푟2 휚 −휚 휔 2푥 Sedimentation 푣 = 푠 푙 푣 = 푠 푙 9 휂 9 휂 푣휚푙 Reynold’s number 푅푒 = 휂 휋푟4Δ푝 Poiseuille’s law 푉 = 푡 8휂푙