Fluids

Fluids in Motion

In steady flow the velocity of the fluid particles at any point is constant as time passes.

Unsteady flow exists whenever the velocity of the fluid particles at a point changes as time passes.

Turbulent flow is an extreme kind of unsteady flow in which the velocity of the fluid particles at a point change erratically in both magnitude and direction.

Types of flowing fluids:

More types of fluid flow

Fluid flow can be compressible or incompressible.

Most liquids are nearly incompressible.

Fluid flow can be viscous or nonviscous.

An incompressible, nonviscous fluid is called an

ideal fluid.

Chapter 11:Fluids

Section 8:

The Equation of Continuity

When a fluid flows…

… mass is conserved

Provided there are no inlets or outlets in a stream

of flowing fluid

The same mass per unit time must flow

everywhere in the stream

The mass of fluid per second that flows through a tube is calledthe mass flow rate.

2222 vAt

m 111

1 vAt

m

Vm

The Equation of Continuity

distance

tvA

222111 vAvA

EQUATION OF CONTINUITY

The mass flow rate has the same value at every position along a tube that has a single entry and a single exit for fluid flow.

SI Unit of Mass Flow Rate: kg/s

Incompressible fluid: 2211 vAvA

The Equation of Continuity

Example Problem

A Pipe of diameter 6.0 cm has fluid flowing through is at 1.6 m/s. How fast is the fluid flowing in an area of the pipe in which the diameter is 3.0 com? How much water flows through the pipe per second?

12

212

1 vrvr

2211 vAvA

sm4.622

211

2 r

rvv

2

015.

03.6.1

m

msm

Problem

The water in a canal flows 0.10 m/s where the canal is 12 m deep and 10 m across. If the depth of the canal is reduced to 6.5 m at an area where the canal narrows to 5.0 m, how fast will the water be moving through this narrower region?

Chapter 11:Fluids

Section 9:

Bernoulli’s Equation

Bernoulli's Theorem

The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous, incompressible fluid in streamline flow.

All other considerations being equal, when a fluid moves faster, the pressure drops

The fluid accelerates toward the lower pressure regions.

According to the pressure-depthrelationship, the pressure is lowerat higher levels, provided the areaof the pipe does not change.

BERNOULLI’S EQUATION

In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:

P1+1

2ρv1

2+ ρ gh1=P2+1

2ρv2

2+ ρ gh2

P1+1

2ρv1

2+ ρ gh1=constant

Expression of conservation of energy –

Energy/Area = Pressure (Force/Area) + PE/Area + KE/Area

Problem

An above ground swimming pool has a hole of radius 0.10 cm in the side 1.0 m below the surface of the water. How fast is the water flowing out of the hole?

Problem

An above ground swimming pool has a hole of radius 0.10 cm in the side 1.0 m below the surface of the water. How far does the water land from the side of the pool if the hole is 1.0 m above the ground?

Problem

Water travels through a 9.6 cm diameter fire hose with a speed of 1.3 m/s. At the end of the hose, the water flows out of a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle?

Problem

Water travels through a 9.6 cm diameter fire hose with a speed of 1.3 m/s. At the end of the hose, the water flows out of a nozzle whose diameter is 2.5 cm. If the pressure in the hose is 350 kPa, what is the pressure in the nozzle in kPa?

Chapter 11:Fluids

Section 10:

Applications of Bernoulli’s Equation

Conceptual Example 14 Tarpaulins and Bernoulli’s Equation

When the truck is stationary, the tarpaulin lies flat, but it bulges outwardwhen the truck is speeding downthe highway.

Account for this behavior.

Example 16 Efflux Speed

The tank is open to the atmosphere atthe top. Find an expression for the speed of the liquid leaving the pipe atthe bottom.

2222

121

212

11 gyvPgyvP

atmPPP 2102 v

hyy 12

ghv 212

1 ghv 21