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Unformatted text preview: Fluids Fluid Statics 7.1 Fluids Density and Pressure Hydrostatic equilibrium Fluids – m aterials that flow when acted upon by e xternal forces. – Liquids – occupy specific volume, incompressible. – Gases take the volume of the container, compressible Densit y Density is the m ass per unit volum e. Pressure Pressure is the Force per unit Area r=
Density of m ateri als m V 3 SI units of kg/m P = F A
A 2 Units N/m Pascal (Pa) Pressure is a scal ar quantity r (kg/m3 ) F Atmospheric pressure (1 atm ) =1.01x105 Pa 2 = 14.7 (pounds/in ) water 1000 o air (20 C) 1.2 olive oil 920 ice 917 Pressure exerted by a f luid The force is exerted perpendicular to the area Hydrostatic equilibrium • The net forces on each part of the fluid is zero. • The fluid is at rest. Pres sure is exerted by the f lui d o n the container wa lls or on adjac ent volume of flui d. The pres sure is the sa me in a ll direc tions. 1 Gravitational equilibrium The forc e of gravity acting on the segm ent equal s the differenc e in force due to pressure at top and bottom . Pressure increases with depth Fup = Fdown (P + dP )A = PA + grAdh Po dP = grdh
dp = g r dh h dF = gdm = g Adh r g P P = Po + rgh W hich container has the highest pressure at the bottom Question 2 A subm arine with a door 1.5 m is trapped at a depth of 100 m below the surfac e of the water. How m uch force m ust be exerted to open the door. The pressure inside is 1atm a b a) a b) b c) c d) all have the sam e pressure Ö c W hy can’t you breath with a long snorkel tube. Scuba equipment delivers air at the ambient pressure Pressure regul at or The pressure difference inside and outside of the lung is too great The lung will collapse. 2 Gauge pressure is the pressure difference from atmospheric Pascal’s Law The change in pressure in a fluid is the sam e everywhere in the fluid. Gauge pressure PP tmospheric = grh a
P Tire pressure is a gauge pressure. (not absolut e pressure) DP 1 DP 2 DP1 = DP2 Hydraulic press
Pascal’s Law Question In a hydraulic lift, a120 cm diameter piston supports a car. If the total mass of the piston and car is 3200 kg what should the diameter of the smaller piston be if a force of 450 N is to maintain the system in equilibrium. F 2 F 1 DP = F1 F = 2 A1 A 2 DP A sm all force on a sm all area c an generate a l arge forc e from a large area (However, the distanc e m oved m ust be larger.) Atmospheric pressure Atm ospheric pressure is due to the weight of the atm ospheric gas above the earth’ surface Pressure in the vacuum is zero Magdeburg sphere P = 0 o 4 3 rmercury = 1.353x10 kg/m P=grh P=9.8(1.353x104 )(0.760) = 1.01x105 Pa Otto von Guericke in Magdeburg G erm any, 1672. Showed the pressure of the atm osphere could hold together two evacuated hem ispheres. 3 Force on a hemisphere due to the atmospheric pressure uur ur d F = Pd A (norm al force) r ur F= ò Pd A
hem is phe re Question Two hem ispheres with diam eter of 35 cm are evacuated. W hat force is required to pull them apart? R r F F = P( pR 2 )
Area of the circle Question A Ushaped tube open at both ends cont ains wat er and a quantity of oil occupying a 2.0 cm length of the tube. If the oil’s density is0.82 tim es that of water, what is the height differenc e h? 4 ...
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