Fluid Mechanics and Surface Tension Quiz

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Questions and Answers

What is the SI unit of pressure?

Pascal (Pa)

What is the equation for pressure?

$P = \frac{F}{A}$

What is the force exerted by the atmosphere on 1 cm2 of our body at sea level, given the atmospheric pressure is 100 kPa?

1000 Pa

Which type of pressure places limits on how deep we can go without needing to encase ourselves inside the protective shell of a submarine?

Ocean pressure Signup and view all the answers

What is the measurement of blood pressure routinely used for?

Medical diagnosis Signup and view all the answers

What is the normal atmospheric pressure at sea level in kilopascals (kPa)?

100 kPa Signup and view all the answers

In the equation $P = \frac{F}{A}$, if the force (F) remains constant, what happens to the pressure (P) if the area (A) is increased?

Pressure decreases Signup and view all the answers

What is the relationship between atmospheric pressure and altitude?

As altitude increases, atmospheric pressure decreases Signup and view all the answers

What is the unit of force in the equation $P = \frac{F}{A}$?

Newton (N) Signup and view all the answers

What is the pressure exerted by a force of 500 N on an area of 2 m2?

250 Pa Signup and view all the answers

What is the relationship between pressure at two points in a liquid?

$\Delta P = \rho g \Delta h$ Signup and view all the answers

What is the formula for material density?

$\rho = m/V$ Signup and view all the answers

What principle states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and the container walls?

Pascal's principle Signup and view all the answers

What is the equation for pressure at a depth in a static liquid?

$P_h = P_{surface} + \rho gh$ Signup and view all the answers

What is a manometer used for?

Measuring pressure Signup and view all the answers

What causes surface tension?

Cohesive forces Signup and view all the answers

What do surfactants do?

Reduce liquid surface tension Signup and view all the answers

What is the formula for interfacial tension?

Not explicitly mentioned in the text Signup and view all the answers

What are cohesive forces responsible for?

Causing surface tension Signup and view all the answers

How are manometers used in measuring pressure?

To measure absolute and gauge pressure of enclosed gases Signup and view all the answers

What is the formula for the height of liquid rising in a thin glass tube due to capillary action?

h = (2*gamma)/(rho gr) Signup and view all the answers

In capillary action, what does a negative meniscus indicate?

The contact angle is less than 90 degrees Signup and view all the answers

What does a positive meniscus indicate in the context of capillary action?

The contact angle is greater than 90 degrees Signup and view all the answers

Which example demonstrates capillary action with a negative meniscus?

Water in a glass tube Signup and view all the answers

In the context of capillary action, what happens when the cohesive forces in the liquid are weaker than the adhesive forces?

The liquid will be pulled slightly up at the edges of the tube Signup and view all the answers

What is the significance of the contact angle being greater than 90 degrees in capillary action?

The liquid tends to 'bead' Signup and view all the answers

What contributes to the rising of sap in trees and blood flow into our capillaries?

Capillary action Signup and view all the answers

In the formula for the height of liquid rising in a thin glass tube, what is the role of the liquid density (rho)?

Determines the height of liquid Signup and view all the answers

What is the relationship between the height of liquid rising in a thin glass tube and the radius of the tube?

Inverse relationship Signup and view all the answers

What is the key factor determining how the liquid behaves in capillary action?

Surface tension Signup and view all the answers

What is the role of pulmonary surfactants in stabilizing alveoli?

Reducing surface tension and equalizing internal pressure in alveoli of different sizes Signup and view all the answers

How does an increase in surfactant concentration affect smaller alveoli?

It reduces surface tension and internal pressure Signup and view all the answers

What is the impact of surfactants on alveoli with slightly different sizes?

They equalize the internal pressure, providing a stable arrangement Signup and view all the answers

What is the effect of surfactants on the diffusion of oxygen into the bloodstream?

They allow the most diffusion of oxygen into the bloodstream Signup and view all the answers

Why is an understanding of fluid flow physics vital in biological systems like the human circulatory system?

To comprehend factors influencing oxygen diffusion Signup and view all the answers

What happens to the internal air pressure in small bubbles due to the lack of pulmonary surfactants?

It increases, leading to breathing difficulties Signup and view all the answers

How does the addition of surfactants affect the surface tension of alveoli?

It reduces the surface tension Signup and view all the answers

What is the consequence of large bubbles getting larger and small bubbles getting smaller due to high internal air pressure?

Breathing difficulties Signup and view all the answers

Why is it undesirable for large bubbles to get larger and small bubbles to get smaller in the lungs?

It causes breathing difficulties Signup and view all the answers

What is the purpose of the alveoli in our lungs?

To allow the most diffusion of oxygen into the bloodstream Signup and view all the answers

What factors does the Poiseuille law's equation include?

Volumetric flow rate, pressure difference, pipe radius, dynamic viscosity, and length of the pipe Signup and view all the answers

Which factor does the Poiseuille law show fluid flow is very sensitive to?

The radius of the vein Signup and view all the answers

What does the flow resistance of blood across a blood vessel depend directly on?

Viscosity and length Signup and view all the answers

What are the categories into which fluid flows can be classified?

Ideal, laminar, and turbulent Signup and view all the answers

What behavior can blood flow exhibit due to its heterogeneous viscous mixture?

Laminar or turbulent behavior Signup and view all the answers

What role does understanding fluid dynamics play in the context of blood flow?

It is important due to its vital role in bodily functions and potential health implications Signup and view all the answers

What does the Poiseuille law describe?

Pressure drop in an incompressible fluid in laminar flow through a long cylindrical pipe Signup and view all the answers

What does the Poiseuille law show about the impact of any constriction in vessels?

It can lead to decreased flow rates, impacting bodily functions such as breathing and heart functioning Signup and view all the answers

What determines the flow resistance of blood across a blood vessel?

Viscosity and length Signup and view all the answers

What are the distinct characteristics and causes of fluid flows?

Ideal, laminar, and turbulent Signup and view all the answers

What is the equation for volume flow rate for an incompressible fluid?

$F = \frac{\Delta V}{\Delta t}$ Signup and view all the answers

What does Bernoulli's principle state?

An increase in fluid velocity is accompanied by a decrease in pressure and/or a decrease in gravitational potential energy. Signup and view all the answers

Under what conditions is Bernoulli’s equation valid?

Negligible viscosity, laminar flow, and steady flow Signup and view all the answers

What is the equation for Bernoulli's principle?

$P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$ Signup and view all the answers

What does the continuity equation relate?

Volume flow rate, area, and velocity of a fluid Signup and view all the answers

In what scenarios can the Equation of Continuity be applied?

Scenarios with multiple pipes joining (branches) to calculate the speed of fluid in each new pipe Signup and view all the answers

What are special cases of Bernoulli’s equation?

Fixed velocity and fixed height scenarios Signup and view all the answers

When is Bernoulli’s equation applicable?

For most liquids and for gases when no expansion or compression is occurring Signup and view all the answers

What do the parameter values at two points on a streamline relate to in Bernoulli’s equation?

Pressure, velocity, and gravitational potential energy Signup and view all the answers

What do the equation of continuity and Bernoulli’s equation provide insights into?

Fluid behavior and flow characteristics Signup and view all the answers

Study Notes

Fluid Mechanics and Surface Tension

Material density is equal to mass divided by volume (ρ = m/V).
Pascal's principle states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid and the container walls.
In a static liquid, pressure at depth depends on surface pressure and the liquid's density and acceleration due to gravity (P_h = P_surface + ρgh).
The relationship between pressure at two points in a liquid is given by ∆P = ρg∆h.
A manometer is a U-shaped tube filled with fluid and relies on Pascal's principle to measure pressure.
The pressure at point 1 is equal to P_A plus the contribution due to the fluid height above (P_1 = P_A + ρgh).
Manometers can be used to calculate absolute and gauge pressure of enclosed gases.
The density of an unknown fluid can be calculated using a manometer and the pressure difference.
Cohesive forces cause surface tension, while adhesive forces can cause capillary action.
Surface tension is defined as the tension force per unit length at the liquid's surface.
Surfactants are substances that reduce liquid surface tension and are important for lung function.
Interfacial tension and contact angle (θ) are affected by the magnitude of adhesive forces between liquids and solids.

Fluid Mechanics Equations and Principles

Volume flow rate, 𝐹, measures the amount of fluid flowing across a surface in a given time, usually in cubic meters per second (𝑚³/𝑠).
The volume flow rate for an incompressible fluid is equal to 𝑭 = ∆𝑽/∆𝒕, which can also be expressed as 𝐹 = 𝐴∆𝑥/∆𝑡 or 𝑭 = 𝑨𝒗, where 𝐴 is cross-sectional area, 𝑣 is fluid velocity, and ∆𝑽 is the change in fluid volume during a period of time ∆𝒕.
Under certain conditions, such as incompressible fluid and no fluid gained or lost, the volume flow rate is constant along a pipe or channel due to the conservation of mass.
The continuity equation, 𝐹𝑖𝑛 = 𝐹𝑜𝑢𝑡, relates the volume flow rate, area, and velocity of a fluid as 𝐹₁ = 𝐹₂ or 𝐴₁𝑣₁ = 𝐴₂𝑣₂.
The Equation of Continuity can be applied to scenarios with multiple pipes joining (branches) to calculate the speed of fluid in each new pipe.
Bernoulli's principle states that an increase in fluid velocity is accompanied by a decrease in pressure and/or a decrease in gravitational potential energy.
Bernoulli’s equation is valid for incompressible fluids under specific conditions, including negligible viscosity, laminar flow, and steady flow, and it can be given by 𝑃 + 1/2𝜌𝑣² + 𝜌𝑔ℎ = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
Another form of Bernoulli's equation relates the parameter values at two points on a streamline, labeled 1 and 2, as 𝑃₁ + 1/2𝜌𝑣₁² + 𝜌𝑔ℎ₁ = 𝑃₂ + 1/2𝜌𝑣₂² + 𝜌𝑔ℎ₂.
Special cases of Bernoulli’s equation include fixed velocity and fixed height scenarios, where the kinetic energy or gravitational potential energy is constant, respectively.
A specific example involves using Bernoulli’s equation to calculate the pressure required to maintain fluid flow within specified parameters in an industrial plant.
Bernoulli’s equation is applicable for most liquids and for gases when no expansion or compression is occurring.
The equation of continuity and Bernoulli’s equation are fundamental principles in fluid mechanics, providing insights into fluid behavior and flow characteristics.

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