Physics and Math 4 Fluids

Physics and Math 4: Fluids Characteristics of Fluids and Solids Fluid Dynamics Fluids: Substances that flow and conform to the shape of their containers, includes liquids and gases. They can exert perpendicular forces but not shear forces. Viscosity: A measure of a fluid’s internal friction. Viscous Drag is a nonconservative force generated by viscosity. Laminar Flow: Smooth and orderly. Solids: Do not flow. They maintain their shape regardless of their container Density: Mass per unit volume of substance. !r = # $ Pressure: A measure of force per unit area; it is exerted by a fluid on the walls of its container and on objects placed in the fluid. Scalar quantity. The pressure exerted by a gas on its container will 𝑃= always be perpendicular to the container walls. & ' Absolute The sum of all pressures at a certain point within a fluid; it is Pressure: equal to the pressure at the surface of the fluid plus the pressure r 𝑔!ℎ due to the fluid itself. 𝑃()(*+=𝑃, + In water, every additional 10m of depth adds » 1 atm to 𝑃()(*+ Gauge The difference between absolute pressure and atmospheric Pressure: pressure. In liquids, gauge pressure is caused by the weight of the liquid above the point of measurement. r !𝑔!𝑧) −𝑃*(4 𝑃01*02= 𝑃−𝑃*(4= (𝑃, +! Turbulent Flow: Rough and disorderly. Poiseuille’s Law: Determines the rate of laminar flow. p 9: D; 𝑄= h ? =𝐴 @A#B 𝑣 𝐴=cross sectional area 𝑣 =velocity Continuity Fluids will flow more quickly through narrow passages Equation: and more slowly through wider ones. 𝑄 =𝑣Q 𝐴Q =𝑣R 𝐴R Bernoulli’s The sum of the static pressure and the dynamic pressure Equation: will be constant between any two points in a closed system. Q Q 𝑃 Q + R !r !𝑣QR + r 𝑔 ℎQ =𝑃R + R !r !𝑣RR + r 𝑔 ℎR Venturi Effect: The velocity of a fluid passing through a constricted area will INCREASE and its static pressure will DECREASE Hydrostatics Pascal’s A pressure applied to an incompressible fluid will be Principle: distributed undiminished throughout the entire volume of the fluid. 𝑃= = &S 'S &T 'T Hydraulic Operate based on the application of Pascal’s principle to Machines: generate mechanical advantage. Archimedes’ When an object is placed in a fluid, the fluid generates a Principle: buoyant force against the object that is equal to the weight of the fluid displaced by the object. 𝐹V = r !𝑉!𝑔 Also, 𝑚 = r !𝑉 and 𝐹 =𝑃!𝐴. Y2Z[\(]^_`abc Y2Z[\(]defghibad jhked = l2\0m(^_`abc ieol2\0m(^_`abc en ieo en p l2\0m (^_`abc en qicao If the max buoyant force is larger than the force of gravity on the object, the object will float. If the max buoyant force is smaller than the force of gravity on the object, the object will sink. If 𝐹V >𝑚)st2u( 𝑔, then the object floats. If 𝐹V <𝑚)st2u( 𝑔, then the object sinks.Specific Gravity: Ratio of density of an object to density of water. r ^_`abc Specific gravity= r qicao Cohesive vs. Fluids experience cohesive forces with other molecules of Adhesive: the same fluid and adhesive forces with other materials. Surface Tension: Cohesive forces give rise to surface tension. Hydraulic Lift: Venturi Tube: The average height of the horizontal tube remains constant, so r 𝑔ℎ remains constant at points 1 and 2. As cross-sectional area decreases from point 1 to point 2, the linear speed must increase. As the dynamic pressure increases, the absolute pressure must decrease at point 2, causing the column of fluid sticking up from the Venturi tube be to be lower at point 2. Fluids in Physiology Circulatory The circulatory system behaves as a closed system with System: nonconstant flow. The nonconstant flow = our pulse. { 𝑣= = ' u*|}\*u )1(~1(u|) [[p[2u(\)Z*+ *|2* 𝑄 =𝑣 𝐴 ∆𝑃 = 𝑄 × 𝑅 = cardiac output × resistance∆𝑃=𝑣 𝐴 𝑅 Pressure is directly related to velocity, area, and resistance. Area is inversely related to resistance and velocity. Cross-sectional area& Þ Resistance¯ and/or velocity¯ Breathing: Inspiration and expiration create a pressure gradient not only for the respiration system, but for the circulatory system too. Alveoli: Air at the alveoli has essentially zero speed. 𝑃= &S = 'S &T ' 'T T 𝐹R =𝐹 Q (' ) S