Podcast
Questions and Answers
What does the term $
ho$ represent in Bernoulli's Equation?
What does the term $ ho$ represent in Bernoulli's Equation?
- Density of the fluid (correct)
- Height of the fluid column
- Viscosity of the fluid
- Velocity of the fluid
Which of the following describes the type of flow characterized by low Reynolds Number?
Which of the following describes the type of flow characterized by low Reynolds Number?
- Laminar flow (correct)
- Turbulent flow
- Supercritical flow
- Transitional flow
In the context of fluid dynamics, what does Torricelli's Law relate to?
In the context of fluid dynamics, what does Torricelli's Law relate to?
- The speed at which a fluid exits an orifice (correct)
- The impact of viscosity on flow resistance
- The pressure distribution in static fluids
- The relationship between fluid velocity and pressure difference
Which of the following best describes how viscosity affects flow resistance?
Which of the following best describes how viscosity affects flow resistance?
What is a defining characteristic of turbulent flow compared to laminar flow?
What is a defining characteristic of turbulent flow compared to laminar flow?
What condition must be met for Bernoulli's equation to simplify to hydrostatics?
What condition must be met for Bernoulli's equation to simplify to hydrostatics?
What does Torricelli's law describe about the speed of fluid exiting an orifice?
What does Torricelli's law describe about the speed of fluid exiting an orifice?
In the context of fluid dynamics, which of the following best defines viscosity?
In the context of fluid dynamics, which of the following best defines viscosity?
Which flow pattern is characterized by smooth, orderly fluid motion?
Which flow pattern is characterized by smooth, orderly fluid motion?
When considering fluid flow in a horizontal pipe where fluid height does not change, which form of Bernoulli's equation applies?
When considering fluid flow in a horizontal pipe where fluid height does not change, which form of Bernoulli's equation applies?
What does the Reynolds Number indicate in fluid dynamics?
What does the Reynolds Number indicate in fluid dynamics?
Which of the following statements aligns with Torricelli's Law?
Which of the following statements aligns with Torricelli's Law?
How does viscosity affect flow resistance in fluids?
How does viscosity affect flow resistance in fluids?
Which flow pattern is characterized by smooth, orderly motion of fluid particles?
Which flow pattern is characterized by smooth, orderly motion of fluid particles?
In hydrostatics, which statement accurately describes pressure?
In hydrostatics, which statement accurately describes pressure?
Flashcards
Hydrostatic Equation
Hydrostatic Equation
Bernoulli's equation when fluid is stationary or flow is steady (v1 = v2). Pressure at one point plus the product of fluid density, gravity, and height equals the pressure at another point plus the same product.
Bernoulli's Equation (Horizontal Pipe)
Bernoulli's Equation (Horizontal Pipe)
Bernoulli's equation when fluid is flowing horizontally (h1 = h2). Pressure at one point plus half the fluid density times velocity squared equals the pressure at another point plus the same.
Torricelli's Equation
Torricelli's Equation
Calculates the velocity (V) of a liquid flowing out of a hole in a tank due to gravity, directly proportional to the square root of vertical distance(h) from the liquid surface to the hole and the square root of (2 times acceleration due to gravity).
Torricelli's Law
Torricelli's Law
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Steady flow
Steady flow
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What are fluids?
What are fluids?
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Fluid Dynamics
Fluid Dynamics
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Pressure
Pressure
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Viscosity
Viscosity
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Bernoulli's Equation
Bernoulli's Equation
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Total Energy in Fluids
Total Energy in Fluids
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Pressure Energy
Pressure Energy
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Kinetic Energy in Fluids
Kinetic Energy in Fluids
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Potential Energy in Fluids
Potential Energy in Fluids
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Study Notes
Fluid Dynamics
- Fluids include liquids and gases
- Ideal fluid: A fluid that doesn't resist shear stress, meaning no friction between layers
- Laminar flow: Smooth, regular fluid flow
- Turbulent flow: Irregular, fluctuating fluid flow
- Continuity equation: The rate of mass entering a system equals the rate leaving
- Bernoulli's equation: Used to analyze fluid motion, relating pressure, height, and velocity. P₁ + pgh₁ + (1/2)ρv₁² = P₂ + pgh₂ + (1/2)ρv₂²
Torricelli's Law
- Calculates fluid velocity emerging from an opening
- Velocity is proportional to the square root of the height difference and twice the acceleration due to gravity
- v = √(2gh)
Viscosity
- Resistance of a fluid to flow
- Coefficient of viscosity (η): Degree of fluid resistance to flow under applied force
Reynolds Number
- Important quantity to predict fluid flow types (laminar or turbulent)
- Defined as R = (ρVD)/η where:
- ρ = fluid density
- V = average flow velocity
- D = pipe diameter
- η = dynamic viscosity
- R < 2000: Laminar flow
- R > 3000: Turbulent flow
- 2000 < R < 3000: Transition region (unstable flow)
Blood Flow in the Circulatory System
- Blood is a viscous fluid pumped through arteries and veins by the heart
- Blood flow is mostly laminar, not turbulent
- Velocity highest at center of a blood vessel
- Velocity = (P₁ - P₂)(a² - r²)/(4ηl) (Poiseuille's Law)
- a= inner radius of the vessel
- η = viscosity
- l = the length across which a pressure difference exists
- (P₁ - P₂) = pressure difference between the ends of the vessel
Measuring Blood Pressure
- Main artery in upper arm used for measurement
- Inflatable cuff placed around arm to stop blood flow
- Cuff pressure slowly decreases
- Systolic pressure: First sound recorded
- Diastolic pressure: Sound of turbulent flow stops
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