ENERGY EQUATION for Non-uniform Flows

ENERGY EQUATION for Non-uniform Flows

V

Mean Velocity:

=

=

1

1 3

Kinetic Energy Correction Factor:

=

V

Modified Energy Equation (by using Reynolds Transport Theorem for energy)

1

+

1

+ 112 2

+

=

2

+ 2

+ 222 2

+

+

V1 and V2 are the mean velocities at stations 1 and 2

=

=

=

=

CE319F, UT Austin (S.A. Kinnas, 2020)

Energy Equation & Examples

1

Example 7.1

for Laminar or Turbulent Pipe Flows

For laminar flows: 2

= 1 -

Mean Velocity:

=

1

=

1 2

2

=

2

Kinetic Energy Correction Factor:

1 3

=

1

3

=

2

0

2 = 2

For uniform flows:

= 1

For turbulent flows: = 1.05 - 1.07 (we often use = 1 for simplicity)

CE319F, UT Austin (S.A. Kinnas, 2020)

Energy Equation & Examples

2

Example 7.2

ENERGY EQUATION

1

+

1

+ 112 2

+

=

2

+

2

+

222 2

+

+

=

=

=

=

2 = = 2

(for pipes)

Darcy-Weisbach equation f: resistance coefficient or friction factor

CE319F, UT Austin (S.A. Kinnas, 2020)

Energy Equation & Examples

3

Example 7.3

ENERGY EQUATION

1

+ 1

+

112 2

+

=

2

+

2

+

222 2

+

+

=

=

=

=

1 hp= 550 lbf ft/sec

CE319F, UT Austin (S.A. Kinnas, 2020)

1 W = 1 N m/sec

Energy Equation & Examples

1 hp = 0.746 kW

4

Example 7.4

ENERGY EQUATION

1

+

1

+ 112 2

+

=

2

+

2

+

222 2

+

+

=

=

=

=

CE319F, UT Austin (S.A. Kinnas, 2020)

Energy Equation & Examples

5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download