6. Find kinetic energy per cubic meter of flowing blood (V = 1 m³) in aorta for individual at rest. Suppose flow rate is about Q = 5 liter/min, radius of aorta R = 1 cm. The density of blood is p =1.05-10° kg/m³. MOTION OF FLUIDS (part II) M Theory Constants n = 4- 10-3 Parsec is viscosity of blood; p= 1,05 - 10° kg/m blood density; g = 9,8 m/sec is free fall acceleration. hz Formulas 1. Law of energy conservation for fluid: E = Ex + Ep + E, = const, Here Eg fluid intemal energy. is fluid kinetic energy (m = pV); E, = mgh is fluid potential energy; E, = PV is 2. Bernoulli's Equation The relationship between pressure and velocity in fluids is described quantitatively by Bernoulli's equation, named after its discoverer, the Swiss scientist Daniel Bemoulli (1700–1782). Bemoulli's equation states that for an incompressible, frictionless fluid, the following sum is constant: + pgh + P = const, where P is the absolute pressure, p is the fluid density, v is the velocity of the fluid, h is the height above some reference point, and g is the acceleration due to gravity. If we follow a small volume of fluid along its path, various quantities in the sum may change, but the total remains constant. Let the subscripts 1 and 2 refer to any two points along the path that the bit of fluid follows; Bernoulli's equation becomes: Pri + pgh, + P, = i+ pghz + P.. 1.1 Bemoulli's Equation for static fluid, when v, = v2: pgh, + P, = pghz + P2 Po AP PA R2 P R Pieg - Pneart = PgAh Pheart - Phead = pgAh and Pa 1.2 Bemoulli's Equation at constant height h, = h2: pvž. -+ P =- + P2 3. Laminar and turbulent flow, Re Laminar flow is characterized by the smooth flow of the fluid in layers that do not mix. Turbulent flow, or turbulence, is characterized by eddies and swirls that mix layers of fluid together. An indicator called the Reynolds number Re can reveal whether flow is laminar or turbulent. For flow in a tube of uniform diameter, the Reynolds number is defined as: Laminar Turbulent Transitional- oscillates between laminar and turbulent pvd Re =
6. Find kinetic energy per cubic meter of flowing blood (V = 1 m³) in aorta for individual at rest. Suppose flow rate is about Q = 5 liter/min, radius of aorta R = 1 cm. The density of blood is p =1.05-10° kg/m³. MOTION OF FLUIDS (part II) M Theory Constants n = 4- 10-3 Parsec is viscosity of blood; p= 1,05 - 10° kg/m blood density; g = 9,8 m/sec is free fall acceleration. hz Formulas 1. Law of energy conservation for fluid: E = Ex + Ep + E, = const, Here Eg fluid intemal energy. is fluid kinetic energy (m = pV); E, = mgh is fluid potential energy; E, = PV is 2. Bernoulli's Equation The relationship between pressure and velocity in fluids is described quantitatively by Bernoulli's equation, named after its discoverer, the Swiss scientist Daniel Bemoulli (1700–1782). Bemoulli's equation states that for an incompressible, frictionless fluid, the following sum is constant: + pgh + P = const, where P is the absolute pressure, p is the fluid density, v is the velocity of the fluid, h is the height above some reference point, and g is the acceleration due to gravity. If we follow a small volume of fluid along its path, various quantities in the sum may change, but the total remains constant. Let the subscripts 1 and 2 refer to any two points along the path that the bit of fluid follows; Bernoulli's equation becomes: Pri + pgh, + P, = i+ pghz + P.. 1.1 Bemoulli's Equation for static fluid, when v, = v2: pgh, + P, = pghz + P2 Po AP PA R2 P R Pieg - Pneart = PgAh Pheart - Phead = pgAh and Pa 1.2 Bemoulli's Equation at constant height h, = h2: pvž. -+ P =- + P2 3. Laminar and turbulent flow, Re Laminar flow is characterized by the smooth flow of the fluid in layers that do not mix. Turbulent flow, or turbulence, is characterized by eddies and swirls that mix layers of fluid together. An indicator called the Reynolds number Re can reveal whether flow is laminar or turbulent. For flow in a tube of uniform diameter, the Reynolds number is defined as: Laminar Turbulent Transitional- oscillates between laminar and turbulent pvd Re =
College Physics
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ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter12: Fluid Dynamics And Its Biological And Medical Applications
Section: Chapter Questions
Problem 57PE: What is the greatest average speed of blood flow at 37° C in an artery of radius 2.00 mm if the flow...
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