Fluid Mechanics: Flow and Viscosity Concepts
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Questions and Answers

What is the primary factor that opposes relative motion between fluid molecules in a real fluid?

  • Inertia
  • Pressure gradient
  • Viscous friction (correct)
  • Surface tension

    • In laminar flow, the fluid velocity is highest at the walls of the pipe.

    False (B)

    What does Poiseuille’s law describe?

    The flow rate of fluid through a channel.

    As the viscosity of a fluid __________, its flow rates decrease.

    <p>increases</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Viscous friction = Opposes relative motion in real fluids Laminar flow = Fluid flows smoothly in parallel layers Viscosity = A measure of a fluid's resistance to flow Poiseuille's law = Governs the flow rate in cylindrical pipes</p> Signup and view all the answers

    According to Poiseuille's law, how does the flow rate (Q) relate to the radius (r) of the tube?

    <p>Q is directly proportional to r^4 (B)</p> Signup and view all the answers

    As the temperature of a fluid increases, its viscosity also increases.

    <p>False (B)</p> Signup and view all the answers

    What term is used to describe a fluid that flows without friction?

    <p>Ideal fluid</p> Signup and view all the answers

    Which of the following best describes flow rate (Q)?

    <p>The volume of fluid flowing past a point in a pipe per unit time (D)</p> Signup and view all the answers

    According to Bernoulli's equation, the fluid must be compressible.

    <p>False (B)</p> Signup and view all the answers

    What happens to the velocity of a fluid if the cross-sectional area is halved?

    <p>The velocity doubles.</p> Signup and view all the answers

    The flow rate (Q) can be calculated using the equation Q = A × _____

    <p>v</p> Signup and view all the answers

    Match the following terms with their correct descriptions:

    <p>Incompressible fluid = Fluid with constant density Non-viscous fluid = Fluid that experiences no mechanical energy loss due to friction Streamline flow = Smooth and orderly fluid motion Steady state flow = Flow characteristics do not change over time</p> Signup and view all the answers

    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?

    <p>0.1 m/s (D)</p> Signup and view all the answers

    Bernoulli’s equation applies to turbulent flow conditions.

    <p>False (B)</p> Signup and view all the answers

    The equation that denotes the conservation of mass in fluid flow is known as the _____ equation.

    <p>continuity</p> Signup and view all the answers

    What happens to a fluid's flow when its velocity is increased past a critical point?

    <p>The flow becomes turbulent (B)</p> Signup and view all the answers

    In a cylindrical pipe, the Reynolds number is generally less than 2000 for turbulent flow.

    <p>False (B)</p> Signup and view all the answers

    What is the relationship between Q2 and Q1 given Q2 = 0.1Q1?

    <p>Q2 is one-tenth of Q1</p> Signup and view all the answers

    Turbulent flow is characterized by ________ and whirls that mix layers of fluid together.

    <p>eddies</p> Signup and view all the answers

    Which of the following factors causes turbulence in fluid flow?

    <p>Obstruction or sharp corners (D)</p> Signup and view all the answers

    Match the following flow characteristics with their types:

    <p>Laminar flow = Less resistance Turbulent flow = More resistance</p> Signup and view all the answers

    The formula involving diameter, density, viscosity, and Reynolds number defines the critical flow velocity (______.

    <p>vc</p> Signup and view all the answers

    Reynold's number for most fluids typically ranges between 1000 and 2000.

    <p>False (B)</p> Signup and view all the answers

    What is the primary function of arterioles in the circulatory system?

    <p>To regulate blood flow to specific regions in the body (D)</p> Signup and view all the answers

    Systolic pressure is the lowest blood pressure between heartbeats.

    <p>False (B)</p> Signup and view all the answers

    What is the normal reading for diastolic pressure, often expressed as part of blood pressure?

    <p>80 torr</p> Signup and view all the answers

    The _______ carries oxygenated blood away from the left chamber of the heart.

    <p>aorta</p> Signup and view all the answers

    What term describes the pressure of blood at the peak of a pulse?

    <p>Systolic pressure (D)</p> Signup and view all the answers

    Match the following components of the circulatory system with their functions:

    <p>Capillaries = Gas exchange Arterioles = Regulating blood flow Venules = Transporting blood to veins Aorta = Carrying oxygenated blood away from the heart</p> Signup and view all the answers

    Blood flows to the body in continuous streams without any pulses.

    <p>False (B)</p> Signup and view all the answers

    As blood flows through the circulatory system, energy is dissipated by expansion and contraction of _______ walls.

    <p>arterial</p> Signup and view all the answers

    What is the average blood pressure in the capillaries?

    <p>30 torr (C)</p> Signup and view all the answers

    The movement of blood through the veins is solely dependent on the pumping action of the heart.

    <p>False (B)</p> Signup and view all the answers

    What happens to blood pressure as it flows from the heart to the capillaries?

    <p>It decreases.</p> Signup and view all the answers

    The average arterial blood pressure supports a column of blood ____ cm high.

    <p>129</p> Signup and view all the answers

    Match the following components to their descriptions:

    <p>Aorta = Main artery with large radius Arterioles = Smaller arteries with increased resistance Veins = Carry blood back to the heart Valves = Ensure one-way flow in veins</p> Signup and view all the answers

    What is the total blood flow rate at rest?

    <p>5 liters/min (D)</p> Signup and view all the answers

    The pressure drop in the main arteries becomes negligible during exercise.

    <p>True (A)</p> Signup and view all the answers

    What happens to blood pressure as it moves from the arteries to the veins?

    <p>It drops significantly.</p> Signup and view all the answers

    What is the density of blood?

    <p>1.05 g/cm3 (C)</p> Signup and view all the answers

    The average arterial pressure in the feet of an erect person is less than that at the heart.

    <p>False (B)</p> Signup and view all the answers

    What causes a person to feel momentarily dizzy when they jump up from a prone position?

    <p>A sudden decrease in the blood pressure of the brain arteries.</p> Signup and view all the answers

    The average pressure at the head of an erect person is calculated using the formula Phead = P heart - 𝜌 𝑔 ℎ, where g represents __________.

    <p>acceleration due to gravity</p> Signup and view all the answers

    Match the following scenarios with their corresponding blood pressure calculations:

    <p>Phead = P heart - 𝜌 g h Pfeet = P heart + 𝜌 g h Normal condition in veins = Blood pressure in veins is lower than in arteries Dizziness upon standing = Temporary decrease in brain blood flow</p> Signup and view all the answers

    What happens to blood pressure in the legs when a person stands motionless?

    <p>It increases due to blood accumulation. (C)</p> Signup and view all the answers

    Calculate the arterial blood pressure in the head of an erect person who is 50 cm above the heart. Use the given values.

    <p>8.2 x 10^3 Pa</p> Signup and view all the answers

    Most animals have the same range of blood pressure as humans.

    <p>True (A)</p> Signup and view all the answers

    Flashcards

    Flow Rate (Q)

    The volume of fluid passing a point in a pipe per unit time.

    Equation of Continuity

    The product of the cross-sectional area and the velocity of an incompressible fluid remains constant.

    Bernoulli's Equation

    The equation that describes the conservation of energy in a fluid flowing in a streamline, steady-state, and non-viscous manner.

    Streamline Flow

    A type of fluid flow where every particle follows the same path, without crossing each other.

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    Turbulent Flow

    A type of fluid flow where the velocity and pressure fluctuate randomly, creating unpredictable patterns.

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    Incompressible Fluid

    A fluid that doesn't change in density, even under pressure.

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    Non-Viscous Fluid

    A fluid with no internal friction or resistance to flow. It's a theoretical concept.

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    Steady-State Flow

    A flow condition where the fluid properties, like velocity and pressure, don't change with time.

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    Viscosity

    The resistance to flow within a fluid caused by the friction between its molecules. It's essentially the 'stickiness' of a fluid.

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    Poiseuille's Law

    A law describing the rate of fluid flow through a cylindrical tube, considering viscosity. It shows how flow rate is affected by pressure difference, tube radius, and fluid viscosity.

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    Laminar Flow

    A specific type of fluid flow where the fluid moves in parallel layers, with no mixing between layers. Each layer flows at a constant speed.

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    Coefficient of Viscosity (η)

    The coefficient of viscosity (η) measures how resistant a fluid is to flow. It's higher for thicker fluids like honey and lower for thinner fluids like water.

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    Viscosity and Temperature

    Viscosity increases as temperature decreases. This means cold fluids are 'stickier' or more viscous.

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    Flow Rate and Radius

    According to Poiseuille's Law, flow rate (Q) is extremely sensitive to changes in the radius of the tube. A small change in radius has a large impact on flow.

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    Pressure and Flow Rate

    Fluid flow is affected by the pressure difference between the two ends of the tube. A greater pressure difference results in faster flow.

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    Reynolds Number (ℛ)

    The dimensionless quantity used to predict whether the flow of a fluid will be laminar or turbulent.

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    Critical Velocity (vc)

    The critical velocity of a fluid flowing through a cylindrical pipe, above which the flow becomes turbulent.

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    Density of a fluid

    A fluid with high density is more resistant to changes in motion. A fluid with low density is less resistant to changes in motion.

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    Causes of Turbulence

    Obstruction or sharp corners can cause turbulent flow by disrupting the smooth flow of the fluid.

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    Aorta

    The largest artery in the body, carrying oxygenated blood from the left ventricle of the heart to the rest of the body.

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    Smaller Arteries

    Smaller arteries that branch off from the aorta, delivering oxygenated blood to specific regions of the body.

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    Arterioles

    The smallest arteries, responsible for regulating blood flow to different tissues.

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    Capillaries

    Extremely thin blood vessels where gas exchange occurs directly between blood and tissues.

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    Venules

    Small veins that collect deoxygenated blood from capillaries.

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    Veins

    Larger blood vessels that carry deoxygenated blood back to the heart.

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    Systolic Pressure

    The maximum pressure in the arteries during heart contraction (systole).

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    Diastolic Pressure

    The minimum pressure in the arteries between heart contractions (diastole).

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    Pressure Drop in Blood Flow

    The pressure fluctuations in blood flow decrease as blood moves away from the heart due to energy losses.

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    Pressure in Capillaries

    The pressure in the capillaries is much lower than in the arteries (around 30 torr) because of the resistance to flow in the blood vessels.

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    Valves in Veins

    Veins have valves that prevent backflow of blood, ensuring that blood moves towards the heart.

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    Pressure Drop in Arteries

    The pressure drop along the main arteries is relatively small because they have a large radius.

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    Blood Flow Rate (Q)

    The rate of blood flow (Q) through the body varies depending on the level of physical activity.

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    Pressure in Arterioles

    The average pressure at the entrance to the arterioles is about 90 torr, a slight drop from arterial pressure.

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    Pressure Drop in Arterioles

    The pressure drop through the arterioles is significant (about 60 torr), leading to a lower pressure in the capillaries.

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    Constant Arterial Pressure

    Since the pressure drop in the main arteries is small, the arterial pressure is fairly constant throughout the body when in a horizontal position.

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    Blood Pressure in the Head

    Blood pressure in the head is lower than in the heart due to gravitational force acting on the blood column.

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    Blood Pressure in the Feet

    Blood pressure at the feet is higher than in the heart due to the weight of the blood column pushing down.

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    Cardiovascular System's Response

    The cardiovascular system adjusts to changes in body position by regulating blood flow to maintain proper pressure.

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    Dizziness After Standing Up

    Feeling dizzy after standing up suddenly is caused by a temporary drop in blood pressure in the brain.

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    Vein vs. Artery Pressure

    The blood pressure in veins is lower than in arteries.

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    Blood Pooling in Legs

    Blood pooling can occur in legs when standing still due to the weight of the blood pushing down.

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    Blood Pressure in Animals

    Blood pressure in most animals is similar to humans due to the same physiological mechanisms.

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    Hydrostatic Force in Blood Pressure

    The force exerted by the weight of the blood column contributes to the blood pressure at different points in the body.

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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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    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.

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