Fluids

Question 1

Problems involving fluids

Answer 1

standing fluid, think forces; moving fluid, think energy.

Question 2

Fluid

Answer 2

is a liquid or gas. molecular bonds in a fluid are constantly breaking and reforming due to the high kinetic energy of the molecules.

Question 3

Density (p)

Answer 3

Intensive property; the “heaviness” of a fluid, defined as how much mass the fluid contains in a specified volume (V).

p = m/V

Units, kg/m³

Question 4

Compressing a fluid

Answer 4

changes its volume without changing its mass, thus changing the density of the fluid.

Gases compress more easily than liquids.

Gases change their volume (and thus their density) as described by the ideal gas law: PV = nRT.

Question 5

Specific gravity (S.G.)

Answer 5

the density of a substance compared to the density of water.

S.G. = p_substance/p_{<span>water</span>}

p_water = 1000 kg/m^{<span>3</span>} = ​1 g/cm³

S.G. < 1 indicates a substance lighter than water; S.G. > 1 indicates a substance heavier than water.

Question 6

Fluid Pressure

Answer 6

is the pressure experienced by the object as a result of the impulse of molecular collisions.

P = F/A

Unit, Pascal (Pa)

Question 7

Gauge Pressure

Answer 7

is a measure of the pressure compared to local atmospheric pressure.

Question 8

Fluid at rest

Answer 8

experiences only forces perpendicular to its surface.

at any given depth, the pressure is equal to the weight of the fluid above a disk with area A divided by the area of the disk.

Fluid at rest with uniform density in sealed container, P = pgy, where y is the depth of the fluid.

Open the sealed container and expose to the atmosphere, add atmospheric pressure.

When using meters and kg, measure atmospheric pressure in pascals (Pa).

P_atm = 101,000 Pa

Question 9

Pascal’s principle

Answer 9

states that pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished throughout that fluid.

Question 10

Hydraulic Lift

Answer 10

a simple machine that works via pascal’s principle.

two pistons and a container enclose a standing incompressible fluid.

F₁d₁ = F₂d₂

F₁/A₁ = F₂/A₂

Question 11

Buoyant Force

Answer 11

force exerted by a standing fluid on any object that is floating, submerged, or sunk in the fluid.

Within a fluid at rest, both pressure and force increase with depth.

Reaches its max value when the object is fully submerged.

F_b = pgA(change in)h = p_fluidV_{fluid displaced}g

Question 12

Archimedes Principle

Answer 12

the upward buoyant force is equal in magnitude to the weight of the displaced fluid.

F_B = (m_fluid/V_fluid) (V_fluid) (g) = m_fluidg

Question 13

The Case of the Floating Object

Answer 13

If the upward buoyant force becomes equal to the downward force of gravity at any point before the object is fully submerged, the object floats.

F_b=p_fluid V_fluid g=m_fluid g=F_G=m_object g

Fraction of object submerged = p_object/p_fluid = V_fluid/V_object

An object only floats when its density is less than the density of the fluid on which it floats.

Displaces volume of fluid with mass equal to its own mass.

Question 14

The Case of the Submerged Object

Answer 14

density of the object is equal to the density of the fluid in which it is submerged.

displaces volume of fluid with mass equal to its own mass and equal to its own volume.

experiences F_b equal to F_G

Question 15

The Case of the Sunk Object

Answer 15

has density greater than the density of the fluid.

displaces volume of fluid equal to its own volume.

experience F_b less than F_{<span>G</span>}.

Question 16

Molecules of a moving fluid have two types of motion:

Answer 16

1. random translational motion that contributes to fluid pressure as in a fluid at rest.
2. uniform translational motion shared equally by all the molecules at a given location in a fluid. (does not contribute to fluid pressure)

Question 17

Ideal fluids differ from real fluids in the following ways:

Answer 17

1. Ideal fluids have no viscosity. Viscosity is a measure of a fluid’s temporal resistance to forces that are not perpendicular to its surface (tendency to resist flow).
2. Ideal fluids are incompressible, with uniform density.
3. Ideal fluids lack turbulence; they experience steady (or laminar) flow.
4. Ideal fluids experience irrotational flow.

Question 18

Blood flow throughout the circulatory system

Answer 18

is usually laminar.

Turbulent flow generates sound waves, which can be used to determine systolic and diastolic blood pressures.

A blood pressure cuff is inflated to a pressure higher than the systolic pressure, preventing blood flow. As the pressure on the cuff decreases below the systolic pressure, blood flow resumes but is turbulent rather than laminar. The pressure at which the sounds associated with turbulence are first heard is recorded as the systolic pressure. As pressure on the cuff decreases below the diastolic pressure, laminar flow resumes. The pressure at which the sounds of turbulence cease is recorded as the diastolic pressure.

Question 19

Continuity Equation

Answer 19

Q=Av, where Q is called the volume flow rate. A is the cross-sectional area of the pipe and v is its velocity (distance of the pipe section/time).

Since ideal fluids are incompressible, their volume remains constant.

Area is inversely proportional to velocity; the narrower the pipe, the greater the velocity.

Question 20

Bernoulli’s equation

Answer 20

restates conservation of energy in terms of densities and pressures (the intensive properties used to describe fluids).

States that the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume of a fluid remain constant throughout that fluid:

P₁ + 1/2 pv₁² + pgh₁ = P₂ + 1/2 pv₂² + pgh₂

v = square root of 2gh

Question 21

Venturi Effect

Answer 21

decrease in pressure that occurs when a fluid flows into a constricted region of a pipe.

Question 22

In a horizontal pipe of constant cross-sectional area, fluid will flow from high pressure to low pressure according to the following equation:

Answer 22

Change in P = QR, where R is resistance to flow.

Question 23

Poiseuille’s Law

Answer 23

The volume flow rate for real fluid in a horizontal pipe with constant cross-sectional area = change in Pressure x (πr⁴/8 x viscosity x pipe Length).

Question 24

Surface Tension

Answer 24

describes the itensity of the intermolecular forces of a fluid per unit length.

is also responsible to the formation of water droplets. The intermolecular forces pull inward, minimizing the surface area by creating a more spherical shape.

is a function of intermolecular forces, so it is affected by temperature of the fluid (higher temperature leads to weaker surface tension).

Question 25

Capillary Action

Answer 25

When fluid is pulled up a thin tube.

Two types of forces acting: the intermolecular forces responsible for surface tension (cohesive forces) and the forces between the molecules of the tube and fluid molecules (adhesive forces).

If cohesive forces are stronger, a convex surface is formed as the fluid is pulled downward.

If adhesive forces are stronger, a concave surface is formed as the fluid is pulled upward.