To Investigate Relationship Between Specific Energy and Depth of Flow

[FAISAL SARDAR] 2009-CIV-122

EXPERIMENT#02 TO INVESTIGATE THE RELATIONSHIP BETWEEN SPECIFICENERGY (S.E) AND DEPTH OF FLOW (Y) IN A LABORATORY FLUME. OBJECTIVE : To study the specific energy as a function of depth of flow for a given discharge ( to ploat E-Y diagram) to compare critical depth of flow determined theoretically & from E-Y diagram .

APPARATUS :  S6 glass sided Tilting lab flume with manometric flow arrangement and slope adjusting scale.  Point gauge (For measuring depth of channel).

RELATED THEORY : FLUME: It is a channel supported above the ground level. .

SPECIFIC ENERGY: S.E if the total energy per unit weight measured relative to the channel’s bed a nd mathematically

E=Y+ Where E = S.E of the per unit weight Y= depth of flow V2/2g = kinetic head or velocity head

[FAISAL SARDAR] 2009-CIV-122

In Term Of Discharge

Q=AV V= E=y+ E= y + V= V=

= , q=V*y

then E= y +

[FAISAL SARDAR] 2009-CIV-122

SPECIFIC ENERGY CURVE It is the plot which shows the variations in S.E as a function of Depth of flow

CRITICAL FLOW : It is the type of flow which take place at a critical depth with minimum specific energy . Type of flow in which froudes number is “1”

FROUD’S NUMBER: It is the ratio of inertial forces to the gravitational forces. Mathematically it is:

Fr =

√

CRITICAL VELOCITY : Velocity corresponding to critical depth

Vc = √ SUB-CRITICAL FLOW: It is the flow with larger depths and less flow velocities or flow at which Froud’s Number is les than 1 .

y > yc , V < VC SUPER CRITICAL FLOW: It is the flow corresponding to the lesser depths and larger flow velocities. And flow will be called as super critical flow for Froud’s Number

y < yc , V VC

[FAISAL SARDAR] 2009-CIV-122

ALTERNATE DEPTHS: For the value of the specific energy other than at the critical point for a constant discharge, there are two water depths.  One is greater than critical depths.  Other is Less than critical depthsThese two depths for a given specific energy are termed as alternate Depths

PROCEDURE:  Maintain the constant discharge in open channel.  For one particular value of flow, find out the water depths at the different locations andcalculate the average depth of flow..  Calculate the specific energy using this relation:  Repeat this by varying the value of slopes.  Draw E –y curves6.  Find out the critical depths and E min

[FAISAL SARDAR] 2009-CIV-122

OBSERVATION & CALCULATION Width of channel = 300mm DEPTH OF FLOW Sr.#

SLOPE DISCHARGE (m3/sec)

q

yc

y1

y2

y3

y avj

AREA

VELOCITY

(m3/sec/m)

m

mm

mm

mm

mm

m2

m/sec

V2/2g

SPECIFIC ENERGY m

1 1/500

0.0080

0.027

0.0417

45.6

50

44.8

46.8

0.014

0.570

0.017

0.063

2 1/300

0.0080

0.027

0.0417

42.5

40

35.5

39.3

0.012

0.678

0.023

0.063

3 1/200

0.0080

0.027

0.0417

31.8

44.6

31

35.8

0.011

0.745

0.028

0.064

4 1/100

0.0080

0.027

0.0417

26

24.5

25.6

25.4

0.008

1.051

0.056

0.082

5 1/6O

0.0080

0.027

0.0417

21.9

21.6

20

21.2

0.006

1.260

0.081

0.102

6 1/5O

0.0080

0.027

0.0417

18.7

21.2

21

20.3

0.006

1.313

0.088

0.108

[FAISAL SARDAR] 2009-CIV-122

E-y DIAGRAM E-Y diagram 0.05

0.045 0.04 0.035 D E 0.03 P T 0.025 H

E VS y

E VS y ( E=y)

(

0.02

m ) 0.015

0.01 0.005 0 0.000

0.020

0.040

0.060 SPECIFIC ENERGY (m)

0.080

0.100

0.120

[FAISAL SARDAR] 2009-CIV-122

E-y DIAGRAM E-Y diagram 0.05 0.045 0.04

yc

V2/2g

0.035 D E 0.03 P T 0.025 H

SUB CRITICAL FLOW

SUPER CRITICAL FLOW

E=y

E VS y E VS y ( E=y)

(

0.02

m ) 0.015

E VS y

0.01

Emin =0.0630

0.005

0 0.0000.0050.0100.0150.0200.0250.0300.0350.0400.0450.0500.0550.0600.0650.0700.0750.0800.0850.0900.0950.1000.1050.1100.115 SPECIFIC ENERGY (m)

[FAISAL SARDAR] 2009-CIV-122

COMMENTS :  Critical dept yc calculated experimentaly is 0.037 m and theoretical is 0.0417 m.  Difference in yc calculated experimentally and theoretically is due to of error in measure discharge .  % difference in yc calculated ( exp & theratically ) is 11 %.  In open channel flow, specific energy (e) is the energy length, or head, relative to the channel bottom.  The bernoulli equation, which originates from a control volume analysis, is used to describe specific energy relationships in fluid dynamics.  If the flow depth is changed in a channel the specific energy of that flow will change .  A given flow can have a large number of specific energy values depending on the flow depth andvelocity. There is one minimum value of specific energy is called the critical specific energy. For any given flow rate there are 2 different sets of depth and velocity which have thesame specific energy.  One of the flow depths (fr < 1) has most of its energy tied up in depth of flow,.  The other flow depth (fr > 1) has most of its energy tied up as velocity head,  Physically, subcritical flow is deep and the velocities are slow. This means subcritical flow has high potential energy and low kinetic energy. Supercritical flow on the other hand tends to be shallow and the velocities are fast. Supercritical flow has low potential energy and high kinetic energy.  In the e-y diagram e–y diagram, it is seen that a line passes through the critical value on each successive discharge curve. This line corresponds to y=2/3E

[FAISAL SARDAR] 2009-CIV-122

HYDROLICS ENGINEERING LAB REPORT

SUBMITTED BY : FAISAL SARDAR 2009-CIV-122 SUBMITTED TO : ENGR, USMAN