A boat has an initial speed of 16 ft>s. If it then increases its speed along a circular path of radius r = 80 ft at the rate of v # = (1.5s) ft>s, where s is in feet, determine the time needed for the boat to travel s = 50 f
PHYSICS 1321 CHAPTER 12 –FLUID MECHANICS 1. Density (ρ) Very important property of material , fluid or solid. 2 or more objects can have same density despite having different masses and volume if they are made of the same material. Mass per unit volume 3 SI unit : kg/m ρ=m/V 2. Pressure in fluid (p) It is the force exerted per unit area. The force exerted is perpendicular to any surface. Scalar Quantity SI unit : 1 Pa = 1 N/m 2 p=(dF)/(dA) 3. Pressure at depth in a fluid Pressure at depth is greater than pressure p whic0 is at surface p=p +0ρgh --------- (1) In a column, the pressure at the top of each liquid column is p . At 0he bottom , the pressure is p. The difference in p and p is ρ0h. 4. Pascal’s Law Pressure applied to an enclosed fluid is transmitted to every potion of the fluid undiminished and equally. p=(F )1(A )1= (F )2(A )2 5. Absolute Pressure and Gauge Pressure Total pressure is p atm . The excess pressure above atmospheric pressure is called gauge pressure . If the pressure applied is less than atmospheric , the gauge pressure is negative. 6. Archimedes’ Principle When a body is submerged in water , it weighs less as compared to when in air. Principle : When a body is completely or partially immersed in fluid , the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. 7. Surface Tension For instance , in a water body , the molecule at the surface is pulled into the bulk liquid . This reduces the liquid’s area on the surface. 8. Fluid Flow An individual particle moves in a fluid and the path is known as flow line. In steady flow , the flow line remains the same. At high flow rates , the flow becomes non steady. 9. Continuity Equation For an incompressible fluid : A v =A1V1 2 2 10.Bernoulli’s Equation p 1 ρgy +1/1ρv 12 = p 2 ρgy +122ρv 22 11.Viscosity Internal friction in fluid that is , the resistance to flow. Example Lava , Viscosity decreases as temperature increases. 12.Turbulence At low flow speeds , flow of a fluid is laminar but when the threshold is exceeded , the flow pattern becomes turbulent.