Find kinetic energy per cubic meter of flowing blood (V = 1 m³) in aorta for individual during intense physical activity. Suppose flow rate is about Q = 25 liter/min, radius of aorta R = 1 cm. The density of blood is p =1.05-10³ kg/m³. 7. 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 =
Find kinetic energy per cubic meter of flowing blood (V = 1 m³) in aorta for individual during intense physical activity. Suppose flow rate is about Q = 25 liter/min, radius of aorta R = 1 cm. The density of blood is p =1.05-10³ kg/m³. 7. 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 =
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Transcribed Image Text:Find kinetic energy per cubic meter of flowing blood (V = 1 m³) in aorta for individual
during intense physical activity. Suppose flow rate is about Q = 25 liter/min, radius of aorta
R = 1 cm. The density of blood is p =1.05-10³ kg/m³.
7.
Transcribed Image Text: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 =
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