Fluid Mechanics PDF

DEPARTMENT OF PHYSICS FLUID MECHANICS BY: EULOGIO S. AUXTERO JR  Recall: DENSITY – a measure of compactness of matter. SPECIFIC GRAVITY - a measure of the density of a substance compared to the density of a reference substance (water). “if a liquid has a specific gravity of 1.2,...

DEPARTMENT OF PHYSICS FLUID MECHANICS BY: EULOGIO S. AUXTERO JR  Recall: DENSITY – a measure of compactness of matter. SPECIFIC GRAVITY - a measure of the density of a substance compared to the density of a reference substance (water). “if a liquid has a specific gravity of 1.2, it means it is 1.2 times as dense as water” Two objects made of the same material have the same density even though they may have different masses and different volumes 2 Recall: 3  Recall: PRESSURE IN A FLUID – a measure of force distribution over an area. ATMOSPHERIC PRESSURE- the pressure of earth’s atmosphere (which varies with weather changes and with elevation. 4  Recall: PRESSURE, DEPTH, and PASCAL’S LAW “the pressure at the depth ℎ is greater than the pressure by an amount ℎ” 5  Recall: PRESSURE, DEPTH, and PASCAL’S LAW “Pressure applied to an enclosed fluid is transmitted undiminished to every portion Of the fluid and walls of the containing vessels” 6  Recall: PRESSURE, DEPTH, and PASCAL’S LAW “Pressure applied to an enclosed fluid is transmitted undiminished to every portion Of the fluid and walls of the containing vessels” 7  Recall: Gauge Pressure, Absolute Pressure, and Atmospheric Pressure GAUGE – pressure of a system above atmospheric pressure ( ABSOLUTE – the total pressure exerted on a system (. 8  Example A manometer tube is partially filled with water. Oil (which does not mix with water) is poured into the left arm of the tube until the oil-water interface is at the midpoint of the tube. Both arms of the tube are open to the air. Find a relationship between the heights ℎ ℎ. 9 BUOYANCY, and Archimedes’s Principle Buoyancy- apparent loss of weight due to an upward force exerted by the fluid called “Buoyant Force”. Question: How much is the upward force? 10 BUOYANCY, and Archimedes’s Principle A 15.0 " solid gold statue is raised from the sea bottom. What is the tension in the hoisting cable (assumed massless) when the statue is (a) at rest and completely underwater and (b) at rest and completely out of the water? 11 FLUID FLOW Note: ideal fluid is incompressible (density cannot change and no internal friction) Laminar Flow Turbulent Flow The continuity Equation! 12 CONTINUITY EQUATION 13 EXAMPLE: Incompressible oil of density 850 $ & % is pumped through a cylindrical pipe at a rate of 9.5 liters per second. (a) The first section of the pipe has a diameter of 8.0 cm. What is the flow speed of the oil? (b) The second section of the pipe has a diameter of 4.0 cm. What are the flow speed and mass flow rate in that section? 14 EXAMPLE: Incompressible oil of density 850 $ & % is pumped through a cylindrical pipe at a rate of 9.5 liters per second. (a) The first section of the pipe has a diameter of 8.0 cm. What is the flow speed of the oil? (b) The second section of the pipe has a diameter of 4.0 cm. What are the flow speed and mass flow rate in that section? 15 BERNOULLI’S EQUATION Relates the pressure, flow speed, and height for flow of an ideal, incompressible fluid.  Essential tool in analyzing plumbing systems  Hydroelectric generating stations  Flight of airplanes 16 BERNOULLI’S EQUATION “States that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow” 17 BERNOULLI’S EQUATION “States that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow” 18