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Questions and Answers
What is the primary factor that opposes relative motion between fluid molecules in a real fluid?
What is the primary factor that opposes relative motion between fluid molecules in a real fluid?
In laminar flow, the fluid velocity is highest at the walls of the pipe.
In laminar flow, the fluid velocity is highest at the walls of the pipe.
False
What does Poiseuille’s law describe?
What does Poiseuille’s law describe?
The flow rate of fluid through a channel.
As the viscosity of a fluid __________, its flow rates decrease.
As the viscosity of a fluid __________, its flow rates decrease.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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According to Poiseuille's law, how does the flow rate (Q) relate to the radius (r) of the tube?
According to Poiseuille's law, how does the flow rate (Q) relate to the radius (r) of the tube?
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As the temperature of a fluid increases, its viscosity also increases.
As the temperature of a fluid increases, its viscosity also increases.
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What term is used to describe a fluid that flows without friction?
What term is used to describe a fluid that flows without friction?
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Which of the following best describes flow rate (Q)?
Which of the following best describes flow rate (Q)?
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According to Bernoulli's equation, the fluid must be compressible.
According to Bernoulli's equation, the fluid must be compressible.
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What happens to the velocity of a fluid if the cross-sectional area is halved?
What happens to the velocity of a fluid if the cross-sectional area is halved?
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The flow rate (Q) can be calculated using the equation Q = A × _____
The flow rate (Q) can be calculated using the equation Q = A × _____
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Match the following terms with their correct descriptions:
Match the following terms with their correct descriptions:
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If the flow rate of blood in the aorta is 5 liters/min, what is the average velocity of blood if the radius of the aorta is 1 cm?
If the flow rate of blood in the aorta is 5 liters/min, what is the average velocity of blood if the radius of the aorta is 1 cm?
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Bernoulli’s equation applies to turbulent flow conditions.
Bernoulli’s equation applies to turbulent flow conditions.
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The equation that denotes the conservation of mass in fluid flow is known as the _____ equation.
The equation that denotes the conservation of mass in fluid flow is known as the _____ equation.
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What happens to a fluid's flow when its velocity is increased past a critical point?
What happens to a fluid's flow when its velocity is increased past a critical point?
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In a cylindrical pipe, the Reynolds number is generally less than 2000 for turbulent flow.
In a cylindrical pipe, the Reynolds number is generally less than 2000 for turbulent flow.
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What is the relationship between Q2 and Q1 given Q2 = 0.1Q1?
What is the relationship between Q2 and Q1 given Q2 = 0.1Q1?
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Turbulent flow is characterized by ________ and whirls that mix layers of fluid together.
Turbulent flow is characterized by ________ and whirls that mix layers of fluid together.
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Which of the following factors causes turbulence in fluid flow?
Which of the following factors causes turbulence in fluid flow?
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Match the following flow characteristics with their types:
Match the following flow characteristics with their types:
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The formula involving diameter, density, viscosity, and Reynolds number defines the critical flow velocity (______.
The formula involving diameter, density, viscosity, and Reynolds number defines the critical flow velocity (______.
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Reynold's number for most fluids typically ranges between 1000 and 2000.
Reynold's number for most fluids typically ranges between 1000 and 2000.
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What is the primary function of arterioles in the circulatory system?
What is the primary function of arterioles in the circulatory system?
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Systolic pressure is the lowest blood pressure between heartbeats.
Systolic pressure is the lowest blood pressure between heartbeats.
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What is the normal reading for diastolic pressure, often expressed as part of blood pressure?
What is the normal reading for diastolic pressure, often expressed as part of blood pressure?
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The _______ carries oxygenated blood away from the left chamber of the heart.
The _______ carries oxygenated blood away from the left chamber of the heart.
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What term describes the pressure of blood at the peak of a pulse?
What term describes the pressure of blood at the peak of a pulse?
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Match the following components of the circulatory system with their functions:
Match the following components of the circulatory system with their functions:
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Blood flows to the body in continuous streams without any pulses.
Blood flows to the body in continuous streams without any pulses.
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As blood flows through the circulatory system, energy is dissipated by expansion and contraction of _______ walls.
As blood flows through the circulatory system, energy is dissipated by expansion and contraction of _______ walls.
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What is the average blood pressure in the capillaries?
What is the average blood pressure in the capillaries?
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The movement of blood through the veins is solely dependent on the pumping action of the heart.
The movement of blood through the veins is solely dependent on the pumping action of the heart.
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What happens to blood pressure as it flows from the heart to the capillaries?
What happens to blood pressure as it flows from the heart to the capillaries?
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The average arterial blood pressure supports a column of blood ____ cm high.
The average arterial blood pressure supports a column of blood ____ cm high.
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Match the following components to their descriptions:
Match the following components to their descriptions:
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What is the total blood flow rate at rest?
What is the total blood flow rate at rest?
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The pressure drop in the main arteries becomes negligible during exercise.
The pressure drop in the main arteries becomes negligible during exercise.
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What happens to blood pressure as it moves from the arteries to the veins?
What happens to blood pressure as it moves from the arteries to the veins?
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What is the density of blood?
What is the density of blood?
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The average arterial pressure in the feet of an erect person is less than that at the heart.
The average arterial pressure in the feet of an erect person is less than that at the heart.
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What causes a person to feel momentarily dizzy when they jump up from a prone position?
What causes a person to feel momentarily dizzy when they jump up from a prone position?
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The average pressure at the head of an erect person is calculated using the formula Phead = P heart - 𝜌 𝑔 ℎ, where g represents __________.
The average pressure at the head of an erect person is calculated using the formula Phead = P heart - 𝜌 𝑔 ℎ, where g represents __________.
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Match the following scenarios with their corresponding blood pressure calculations:
Match the following scenarios with their corresponding blood pressure calculations:
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What happens to blood pressure in the legs when a person stands motionless?
What happens to blood pressure in the legs when a person stands motionless?
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Calculate the arterial blood pressure in the head of an erect person who is 50 cm above the heart. Use the given values.
Calculate the arterial blood pressure in the head of an erect person who is 50 cm above the heart. Use the given values.
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Most animals have the same range of blood pressure as humans.
Most animals have the same range of blood pressure as humans.
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Study Notes
Chapter 8: The Motion of Fluids
- Flow Rate (Q): Defined as the volume of fluid flowing past a point in a pipe per unit time. SI unit is m³/s.
- Equation of Continuity: Q = Av, where Q is the flow rate, A is the cross-sectional area of the tube, and v is the velocity of the fluid. This equation states that the product of the cross-sectional area and velocity of the fluid remains constant in a constant-density fluid. For incompressible fluids, Q1 = Q2, or A₁v₁ = A₂v₂.
Bernoulli's Equation
- Conditions for Applicability: The fluid is incompressible, non-viscous, the flow is streamline, and the velocity of the fluid at any point is constant with time (steady-state flow).
- Bernoulli's Equation: P + ρgh + ½ρv² = constant, where P is the pressure of the fluid, ρ is the fluid's density, g is the acceleration due to gravity, h is the height, and v is the velocity of the fluid. This equation signifies that the sum of pressure, potential energy per unit volume, and kinetic energy per unit volume remains constant from one point of flow to another, in a constant-density, incompressible-fluid.
- Significance: Describes the relationship between velocity, pressure, and elevation in a flowing fluid. Pressure decreases as velocity increases, and elevation increases.
Viscosity and Poiseuille's Law
- Viscosity: A measure of a fluid's internal friction, opposing the relative motion between fluid layers via frictional force, this relationship is proportional to the velocity of flow.
- Poiseuille's Law: Q = πr⁴(P₁ - P₂)/8ηL, where Q is the volumetric flow rate, r is the radius of the cylindrical tube, P₁ and P₂ are the pressures at the two ends, η is the viscosity, and L is the length of the tube.
- Laminar Flow: Fluid flowing in layers where velocity is highest at the center and decreases towards the walls.
- Relates flow rate with pressure difference, radius, viscosity and length of the cylindrical tube.
Blood Flow and Circulation
- Circulatory System: Blood flow in the body can be compared to a plumbing system (the analogy is not perfect). The heart acts as the pump and veins, arteries, and capillaries act as the pipes.
- Pressure and Blood Flow: The pressure in arteries is higher than that in veins when the person is not moving or stationary, blood gathers in the veins of the legs, causing pressure to increase in capillaries and temporary swelling of the legs.
- Factors determining blood flow include blood pressure, pressure drop rate along arteries, viscosity, and the dimensions of the vessels. The blood flow depends on physical activity level.
- Arterial Pressure Drop: Pressure drop in narrower arteries is significant compared to pressure drop in wider-radius arteries.
- Turbulent Flow: Unstable, chaotic flow that is often associated with constrictions in blood vessels. Critical velocity, influenced by density and viscosity, signifies the point of transition from laminar to turbulent flow.
Blood Pressure Measurement
- Measurement: Done by inserting a vertical glass tube into an artery and tracking the rise of blood within it, or by using a cuff with an inflatable balloon around the arm, monitoring the pressure and listening to the flow changes with a stethoscope.
- Systolic/Diastolic Pressure: The maximum (systolic) and minimum(diastolic) pressure in arteries are tracked, usually expressed as a ratio (e.g., 120/80 mmHg).
- Location of Measurement: Typically taken in the arm at approx. heart-level, while ensuring constant pressure.
Arteriosclerosis
- Definition: Thickening and narrowing of arterial walls due to plaque buildup.
- Consequences: Increased resistance to blood flow, potentially leading to heart attack, stroke or other cardiovascular issues. Measurement of flow rate and arterial pressure is crucial for diagnostics.
- Critical Impact: Above 80% stenosis, critical flow rate may result in the heart stop functioning.
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Description
Test your understanding of fluid mechanics with this quiz focusing on flow rates, viscosity, and related laws. Explore concepts such as Poiseuille's law and Bernoulli's equation while matching terms with their definitions. Ideal for students studying fluid dynamics concepts in their physics courses.
