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Fluids Fluids in Motion

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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:

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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.

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Chapter 11: Fluids Section 8: The Equation of Continuity

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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

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

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The Equation of Continuity

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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

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Incompressible fluid: The Equation of Continuity

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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?

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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?

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Chapter 11: Fluids Section 9: Bernoulli’s Equation

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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

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The fluid accelerates toward the lower pressure regions. According to the pressure-depth relationship, the pressure is lower at higher levels, provided the area of the pipe does not change.

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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: Expression of conservation of energy – Energy/Area = Pressure (Force/Area) + PE/Area + KE/Area

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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?

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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?

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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?

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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?

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Chapter 11: Fluids Section 10: Applications of Bernoulli’s Equation

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Conceptual Example 14 Tarpaulins and Bernoulli’s Equation When the truck is stationary, the tarpaulin lies flat, but it bulges outward when the truck is speeding down the highway. Account for this behavior.

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Example 16 Efflux Speed The tank is open to the atmosphere at the top. Find an expression for the speed of the liquid leaving the pipe at the bottom.

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