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ME 200 –Thermodynamics I Spring 2016

Lecture 16: Control Volume Analysis –

Mass Conservation

Yong LiShanghai Jiao Tong University

Institute of Refrigeration and Cryogenics800 Dong Chuan Road Shanghai, 200240, P. R. China

Email : liyo@sjtu.edu.cnPhone: 86-21-34206056; Fax: 86-21-34206056

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Lecture Contents Last lecture

» Ideal Gas Model : u and h depend only on T

» Properties of Ideal Gases

» Polytropic Process

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This lecture

Conservation of Mass for Open System

Flow Energy

The objective of this chapter:

To develop and illustrate the use ofthe control volume forms ofthe conservation of massand conservation of energy principles

Devices such as turbines, pumps, and compressors

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Conservation of Mass

Mass can neither be created nor destroyed

Closed System (Control Mass)» System mass remains constant» i.e. msystem = constant

Open System (Control Volume)» Net mass transfer to or from a system equals the net change in total mass

of the system» i.e. min – mout = Δmsystem

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Mass Flow Rate

Amount of mass flowing through a cross section per unit time (kg/s)

For most cases of practical interest» One-dimensional flow i.e. properties do not vary over the flow area at

each inlet or exit» Velocity and density constant across the cross-section

mass flux:::

Time rate of mass flow perunit of area.

CONCEPTS

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Conservation of Mass

mass rate balance forcontrol volumes withseveral inlets and exits

General form

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Other forms

Conservation of mass principle for one-dimensional open system

Steady state

Integral form

More than 1 inletOr more than 1 outlet

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Flow Energy

Open system (control volume) involves flow of mass across its boundary

Flow energy::: the amount of work required to push the mass into and out of the given system in order to maintain continuous flow

For a fluid at pressure p and specific volume v, specific flow energy is given by

Wflow= pv

CONCEPTS

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Total Energy

Recall: E = U + PE + KE

For non-flowing fluid closed systems, the total specific energy is given by:

For flowing fluid (open systems), the total specific energy is

V2

CONCEPTS

V2 V2pv

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Example 1 Water Flow through a Garden Hose Nozzle A garden hose attached with a

nozzle is used to fill a 10-gal bucket. The inner diameter of the hose is 2 cm, and it reduces to 0.8 cm at the nozzle exit. If it takes 50 s to fill the bucket with water, determine (a) the volume and mass flow rates of water through the hose, and (b) the average velocity of water at the nozzle exit.

a)

b)

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Example 2 Steam is leaving a 4-L pressure cooker whose operating pressure is 150 kPa.

It is observed that the amount of liquid in the cooker has decreased by 0.6 L in 40 min after the steady operating conditions are established, and the cross-sectional area of the exit opening is 8 mm2. Determine (a) the mass flow rate of the steam and the exit velocity, (b) the total and flow energies of the steam per unit mass, and (c) the rate at which energy leaves the cooker by steam.

Assumptions:

1 )steady flow,

2)ΔKE=ΔPE=0,

3)Saturation conditions

4-L

40 min

Liquid -0.6 L

8 mm2

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4-L

40 min

Liquid -0.6 L

8 mm2

Example 2 cont’d

a) the mass flow rate of the steam

the exit velocity

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b) The total and flow energies of the steam per unit mass

c) The energy rate leaving the cooker

4-L

40 min

Liquid -0.6 L

8 mm2