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Learn about density, pressure, buoyant force, blood pressure, and more in this comprehensive physics chapter on fluids. Understand Bernoulli's equation, Pascal's principle, and the behavior of ideal fluids.
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Fluids Liquids and Gases Chapter 11
Units : Density Density is the amount of mass in 1 m3. What is the mass of 5200 cm3 of 1060 kg/m3 blood?
Unit: Pressure Pressure is the force exerted by a fluid on an area of 1 m2.
Air pressure Standard atmospheric pressure at sea level is 101,300 Pa = 1 atmosphere = 1 atm
Example How much force does the air exert on the liquid in the tube that has a 2 cm2 surface area?
pressure difference Pressure at depth in a liquid Pressure is the same everywhere at the same depth. Consider a block of liquid at rest.
Example 4 The Swimming Hole Points A and B are located a distance of 5.5 m beneath the surface of the water. Find the pressures at A and B. A and B are at the same depth so their pressures are the same.
Blood pressure What is the difference in blood pressure between a person's heart and their feet?
Pressure • Points A, B, C, and D are all ... • At the same level. • In the same liquid . • At the same pressure.
no air pressure liquid mercury air pressure Barometer A barometer is an instrument used to measure atmospheric pressure. How tall would mercury be for 101,300 Pa air pressure? For water h = 10.3 m or about 34 feet. A and B are at the same level so their pressures are the same.
Absolute pressure and Gauge pressure Tire pressure is measured in customary units of psi. [ psi means pounds/inch2 ] Inside the tire the gauge pressure is 30 psi above normal atmospheric pressure. Outside the tire atmospheric pressure is 15 psi. Inside the tire the absolute pressure is 45 psi. 30 psi + 15 psi = 45 psi.
Absolute pressure and Gauge pressure gas pressure A and B are at the same level so their pressures are the same.
Open-tube manometer blood-pressure gauge Blood pressure cuff measures a patient's blood pressure in units of the height of mercury in a tube. Blood pressure is gauge pressure.
Measuring blood pressure Blood pressure in the heart should be measured at the same horizontal level as the heart (usually at the upper arm).
Pascal's principle Increasing the pressure at one place in an enclosed fluid increases the pressure by the same amount everywhere in the fluid. This principle explains the operation of all hydraulic systems.
Hydraulic systems • Force on a piston is proportional to the piston area. • Small piston Small force • Large piston Large force
Example 7 A Car Lift Find gauge pressure needed to raise the car.Find force needed at the small piston. Car and large piston weigh 20,000 N. Density of the hydraulic oil is 800 kg/m3. Height h is 2 m. Ignore the weight of the pistons. Small piston r = 0.012 m A = 4.52 x 10-4 m2 Large piston r = 0.15 m A = 0.0707 m2
Archimedes' principle The upward force that fluids exert on partially or fully submerged objects is called a buoyant force. The buoyant force is equal to the weight of the fluid displaced by the object.
Pine wood550 kg/m3 Example 9 A Swimming Raft How deep is the raft submerged?
Pine wood550 kg/m3 Example 9 A Swimming Raft Since the density of the raft was less than the density of the water, the submerged depth was less than the thickness of the raft. If the density of the raft were greater than the water, the raft would sink because it could not displace a weight of water equal to its own weight.
Archimedes' principle The fluid in a charged battery has a higher density than the fluid in a discharged battery. Green ball floats when the fluid density is more than the ball density.
Fluid dynamics: vocabulary Streamlines - paths of fluid particles Steady flow - constant velocity Unsteady flow - variable velocity Turbulent flow - erratically variable velocity Compressible - variable density (example: gases) Incompressible - constant density (example: liquids) Viscous flow - does not flow easily (example: honey) Non-viscous flow - flows easily (example: water) Ideal fluid - incompressible, non-viscous fluid (Our focus will be on the behavior of ideal fluids.)
m Mass Flow Rate unit: Mass flow rate Mass of fluid flowing past a point in one second is called the mass flow rate. The (blue) mass m with velocity v in section 1 will flow past the end of the tube in time Δt.
Continuous flow A single tube with wide and narrow sections has different velocities in each section, but the same mass flow rate.
cross sectional area of 1.6x10-4 m2 cross sectional area of 0.8 x10-4 m2 Example 12 A Garden Hose Hose fills an 8 x 10-3 m3 bucket in 20 seconds.Find the volume flow rate. Find the mass flow rate. Find the velocity for each example.
Pressure changes along a flowing fluid Pressure change provides the net force needed to accelerate the fluid. Pressure must drop to allow the fluid to speed up. Pressure change is due to the difference in depth in the fluid.
Bernoulli's equation for an ideal fluid Bernoulli's equation describes the relationships between pressure, velocity, and height in a flowing fluid. PressureVelocityHeight Based on principles of work and mechanical energy.
Applications for Bernoulli's equation Conceptual Example 14 Tarpaulins and Bernoulli’s Equation When the truck is stationary, the tarpaulin lies flat, but it bulges outward when the truck is speeding down the highway. Explain.
