layers of the fluid moving relative to each of the fluid moving relative to each th



Viscosity Viscosity is the degree of is the degree of internal friction internal friction in the fluid

in the fluid





The internal friction is associated with The internal friction is associated with the

the resistance between two adjacent resistance between two adjacent the

the resistance between two adjacent resistance between two adjacent layers

layers of the fluid moving relative to each of the fluid moving relative to each th

th

other

other

Fluids in Motion Fluids in Motion

Characteristics of an Ideal Fluid



 The fluid is nonviscousThe fluid is nonviscous

–

– There is no internal friction between adjacent layersThere is no internal friction between adjacent layers



 The fluid is incompressibleThe fluid is incompressible

–

– Its density is constantIts density is constant



 The fluid motion is steadyThe fluid motion is steady

–

– Its velocity, density, and pressure do not change in timeIts velocity, density, and pressure do not change in time



 The fluid moves without turbulenceThe fluid moves without turbulence

–

– No eddy currents are presentNo eddy currents are present

Fluids in Motion Fluids in Motion

Equation of Continuity AA AA Equation of Continuity _ AA₁₁vv₁₁ = A= A₂₂vv₂₂



 The product of the crossThe product of the

cross--i l f i

i l f i

sectional area of a pipe sectional area of a pipe and the fluid speed is a pipe is narrow and speed is pipe is narrow and speed is pipe is narrow and speed is pipe is narrow and speed is low where the pipe has a low where the pipe has a large diameter

large diameter



 Av is called the Av is called the flow rateflow rate

Fluids in Motion Fluids in Motion



 The equation is a consequence of The equation is a consequence of conservation conservation of mass

of mass and aand a steady flowsteady flow of mass

of mass and a and a steady flowsteady flow



 A v = constantA v = constant

i i i f

i i i f

–

– This is equivalent to the fact that

of fluid that entersenters one end of the tube in a one end of the tube in a

i i i

i i i ff

given time interval equals

given time interval equals the volumethe volume of of fluid

fluid leavingleaving the tube in the same intervalthe tube in the same interval

 Assumes the fluid is Assumes the fluid is incompressibleincompressible and and

Example 7

A water hose 2.50 cm in diameter is used by a gardener to fill a 30.0-liter bucket.( One liter =1000 cm³) The gardener notices that it take 1.00 min to fill the bucket. A nozzle with an opening of cross-sectional g p g area 0.500 cm²is then attached to the hose. The nozzle is held so that water is projected horizontally from a point 1.00 m above the ground. Over what horizontal distance can the water be projected?

Fluids in Motion Fluids in Motion

Daniel Bernoulli Daniel Bernoulli



 1700 1700 –– 17821782



 Swiss physicist and Swiss physicist and p yp y mathematician

mathematician



 Wrote Wrote HydrodynamicaHydrodynamicayy yy



 Also did work that was Also did work that was the beginning of the

the beginning of the gg gg kinetic theory of gases kinetic theory of gases

Fluids in Motion Fluids in Motion

Bernoulli’s Equation Bernoulli s Equation



 Relates Relates pressurepressure to fluid to fluid speedspeed and and elevationelevation



 Bernoulli’s equation is a consequence of Bernoulli’s equation is a consequence of Conservation of Conservation of Energy

Energy applied to an applied to an ideal fluidideal fluid



 Assumes the fluid is incompressible and nonviscous, and Assumes the fluid is incompressible and nonviscous, and flows in a nonturbulent, steady

flows in a nonturbulent, steady--state mannerstate manner



 States that the States that the sum ofsum of the pressure, kinetic energy per the pressure, kinetic energy per unit volume, and the potential energy per unit volume unit volume, and the potential energy per unit volume has the same value at all points along a streamline

has the same value at all points along a streamline

Fluids in Motion Fluids in Motion

Venturi Tube^文氏管 Venturi Tube^文氏管



 Shows fluid flowing through Shows fluid flowing through a horizontal constricted pipe a horizontal constricted pipe



 Speed changes as diameter Speed changes as diameter changes

changes



 Can be used to measure the Can be used to measure the speed of the fluid flow

speed of the fluid flow



 Swiftly moving fluids exert Swiftly moving fluids exert less pressure than do slowly less pressure than do slowly moving fluids

moving fluids

Example 8

A nearsighted sheriff fires at a cattle rustler with his trusty six-shooter. Fortunately for the rustler, the bullet misses him and penetrated the town water tank, causing a leak. (a) If the top of the tank is open to the

atmosphere, determine the speed at which the water leaves the hole when the water level is 0.500 m above the hole. (b) Where does the stream hit the ground if the hole is 3.00 m above the ground?

Fluids in Motion Fluids in Motion

An Object Moving Through a Fluid



 Many common phenomena can be explained by Many common phenomena can be explained by An Object Moving Through a Fluid

y p p y

y p p y

Bernoulli’s equation Bernoulli’s equation

–

– At least partiallyAt least partiallypp yy



 In general, an object moving through a fluid is In general, an object moving through a fluid is acted upon by a net upward force as the result acted upon by a net upward force as the result acted upon by a net upward force as the result acted upon by a net upward force as the result of any effect that causes the fluid to change its of any effect that causes the fluid to change its direction as it flows past the object

direction as it flows past the object direction as it flows past the object direction as it flows past the object