CEE 367 FLUID MECHANICS LABORATORY

LAB 2 – Forces on a Sluice Gate

Prepared For:

Sayed Abedin

Department of Civil Engineering

University of Nevada, Las Vegas

Prepared By:

Farid Najand

Laboratory Date: 01-31-2013

Submission Date: 02-19-2013

A. Summary

A Sluice gate is a mechanism used to control water flow. The gates often slide vertically on a frame, which allows the water to either flow out of a space or to be contained. Laboratory 2 explores the forces applied on a sluice gate. This experiment helps visualize water pressures at different depths by the control of water flow. Three methods are used to estimate these forces; hydrostatic pressure method, actual pressure method and the momentum theorem method. These methods are applied with the sluice gate completely closed, open .5 inch, and also with the gate open at .75 inch. During the procedure, with the gate completely closed, observations are made and monometer readings are recorded for data. With the gate open, water flow and pressure changes emerge. A water level of 8 inches is maintained in the upstream side while the sluice gate experiences forces acting upon it. Elevation head, piezometric head and pressure head is determined with data collected from the experiment. Based on the results there is a relationship between the measured head and the monometer number. As the monometer number increases, the elevation head also increases.

B. Objective

The main objective of this lab is to analyze the forces acting upon a sluice gate that is necessary for a proper design. Three methods used to estimate these forces are: hydrostatic pressure, actual pressure and momentum theorem. A proper understanding of how these forces act is imperative to the design of an efficient sluice gate.

C. Procedure

Sluice gate experiment will be conducted into three different steps. During each experimental procedure, it is essential to maintain consistently eight inches upstream water level inside the channel. Then place the sluice gate inside the channel and block the water flow completely. Once the Sluice gate is kept on right location, measure the temperature and observe the water pressure from the manometer. The sluice gate has several attached manometer at different depth and record the pressure height against the Sluice gate. Second, place the Sluice gate at half an inch above the channel floor and maintain the same amount of eight inches upstream water flow. Then observe the pressure change and record data. Third, place the sluice gate at .75 inches above the channel floor and once again maintain the same amount of eight inches upstream water flow. Then, observe the pressure change and record data.

D. Data Tables

Method 1 Data - Closed

Width of the channel (m), B= 6”= 0.1524 mWater temperature (°C), T= 23.6

Specific weight of the fluid (N/m3), = 9810Depth of the water level, upstream side (m), h1 = 8” = 0.2032 mFlow rate (m3/s), Q = 0 m3/s

Data Table 1- Sluice Gate Closed

Manometer No. Height Elevation Head Piezometric HeadPressure

HeadInches Meters  Inches Meters Inches Meters Meters

1 0.5 0.0127 0.2 0.0051 7.7 0.19558 0.190482 0.5 0.0127 0.3 0.0076 7.7 0.19558 0.187983 0.5 0.0127 0.5 0.0127 7.7 0.19558 0.182884 0.5 0.0127 1 0.0254 7.7 0.19558 0.170185 0.5 0.0127 1.5 0.0381 7.7 0.19558 0.157486 0.5 0.0127 2 0.0508 7.8 0.19812 0.147327 0.5 0.0127 2.5 0.0635 7.8 0.19812 0.134628 0.5 0.0127 3.5 0.0889 7.8 0.19812 0.109229 0.75 0.0191 4.5 0.1143 7.8 0.19812 0.08382

10 1 0.0254 5.5 0.1397 7.8 0.19812 0.0584211 1 0.0254 7 0.1778 7.8 0.19812 0.0203212 1.25 0.0318 8 0.2032 7.8 0.19812 -0.0050813 1.25 0.0318 10 0.254 7.8 0.19812 -0.05588

Data Result Table 1 -Sluice Gate Closed

Hydrostatic Method

Actual Pressure MethodMomentum

Theorem MethodManometer

Pressure Head

Pressure (Pa) Force (N)

pc 996.696 1 0.19048 1868.6088 3.61665496M1

(m3)0.00314

6F

(N)30.8653627

9 2 0.18798 1844.0838 3.569187313M2

(m3) 0

3 0.18288 1794.0528 3.472353313 F (N)30.8622

64 0.17018 1669.4658 3.2312176675 0.15748 1544.8788 2.990082026 0.14732 1445.2092 2.7971735027 0.13462 1320.6222 2.5560378568 0.10922 1071.4482 2.0737665629 0.08382 822.2742 2.393508632

10 0.05842 573.1002 2.2184479511 0.02032 199.3392 0.77163407

12 -0.00508 -49.8348-

0.241515388

13 -0.05588 -548.1828-

2.656669267Total Force = 29.69006385

Method 2 Data – Open 0.5”

Depth of the water level, upstream side (m), h1 = 8” = 0.2032 m

Depth of the water level, downstream side (m), h2 = 0.5” = 0.0127 m

Difference in the water levels (m), Δ = 7.5” = 0.1905 m

Sluice gate opening (m), t = 0.5” = 0.0127 m

Flow rate (m3/s), Q = .00336

Data Table 2- Sluice Gate Open 0.5"

Manometer No. Height Elevation Head Piezometric Head

Pressure Head

Inches Meters Inches MetersInches Meters Meters

1 0.5 0.0127 0.7 0.0178 5.8 0.14732 0.12952

2 0.5 0.0127 0.8 0.0203 6.4 0.16256 0.14226

3 0.5 0.0127 1 0.0254 6.4 0.16256 0.13716

4 0.5 0.0127 1.5 0.0381 6.9 0.17526 0.13716

5 0.5 0.0127 2 0.0508 7.1 0.18034 0.12954

6 0.5 0.0127 2.5 0.0635 7.2 0.18288 0.11938

7 0.5 0.0127 3 0.0762 7.3 0.18542 0.10922

8 0.5 0.0127 4 0.1016 7.3 0.18542 0.08382

9 0.75 0.0191 5 0.127 7.3 0.18542 0.05842

10 1 0.0254 6 0.1524 7.4 0.18796 0.03556

11 1 0.0254 7.5 0.1905 7.3 0.18542 -0.00508

12 1.25 0.0318 8.5 0.2159 7.4 0.18796 -0.02794

13 1.25 0.0318 10.5 0.2667 7.5 0.1905 -0.0762

Data Result Table 2 -Sluice Gate Open 0.5"

Hydrostatic Method

Actual Pressure Method Momentum Theorem MethodM. # Pressure Head Pressure (Pa) Force (N)

pc 934.4025 1 0.12952 1270.5912 2.459203856 M1 (m3) 0.003183486F (N) 27.12776 2 0.14226 1395.5706 2.701098985 M2 (m3) 0.000640373

3 0.13716 1345.5396 2.604264985 F (N) 24.947938144 0.13716 1345.5396 2.6042649855 0.12954 1270.7874 2.4595835976 0.11938 1171.1178 2.266675087 0.10922 1071.4482 2.0737665628 0.08382 822.2742 1.5914952699 0.05842 573.1002 1.668202986

10 0.03556 348.8436 1.35035962211 -0.00508 -49.8348 -0.19290851712 -0.02794 -274.0914 -1.328334634

Total = 21.77891593

Method 3 Data – Open 0.75”

Depth of the water level, upstream side (m), h1 = 8” = 0.2032 m

Depth of the water level, downstream side (m), h2 = 0.75” = 0.0191 m

Difference in t e water levels (m), Δ = 7.25” = 0.1841 m

Sluice gate opening (m), t = 0.75” = 0.0191 m

Flow rate (m3/s), Q = .00496

Data Table - Sluice Gate Open 0.75"

Manometer No. Height Elevation Head Piezometric Head Pressure Head

Inches Meters Inches Meters Inches Meters Meters1 0.5 0.0127 0.95 0.0241 5.1 0.12954 0.105442 0.5 0.0127 1.05 0.0267 5.8 0.14732 0.120623 0.5 0.0127 1.25 0.0317 6.2 0.15748 0.125784 0.5 0.0127 1.75 0.0444 6.5 0.1651 0.12075 0.5 0.0127 2.25 0.0571 6.9 0.17526 0.118166 0.5 0.0127 2.75 0.0698 7 0.1778 0.1087 0.5 0.0127 3.25 0.0825 7.1 0.18034 0.097848 0.5 0.0127 4.25 0.1079 7.1 0.18034 0.072449 0.75 0.0191 5.25 0.1333 7.1 0.18034 0.04704

10 1 0.0254 6.25 0.1587 7.2 0.18288 0.0241811 1 0.0254 7.75 0.1968 7.2 0.18288 -0.0139212 1.25 0.0318 8.75 0.2222 7.2 0.18288 -0.0393213 1.25 0.0318 10.75 0.273 7.2 0.18288 -0.09012

Data Result Table 3 - Sluice Gate Open 0.75"

Hydrostatic Method

Actual Pressure MethodMomentum Method

Manometer Pressure Head Pressure (Pa) Force (N)

pc 903.0105 1 0.10544 1034.3664 2.00199548 M1 0.0032273F

(N)26.912732 2 0.12062 1183.2822 2.290219032 M2 0.0009391

3 0.12578 1233.9018 2.388192256 F (N) 22.4468574 0.1207 1184.067 2.2917379975 0.11816 1159.1496 2.2435108686 0.108 1059.48 2.050602357 0.09784 959.8104 1.8576938338 0.07244 710.6364 1.3754225399 0.04704 461.4624 1.343243212

10 0.02418 237.2058 0.91821416411 -0.01392 -136.5552 -0.52859971712 -0.03932 -385.7292 -1.869367137

Total = 18.76083173

E. Sample Calculations

Variables Defined:

γ :specific weight of water

pc : Pressure at centroid

h : height sluice gate is submerged

B : width of channel

pi : pressure over the manometer

hi : pressure head

Q : flow rate

M1 : upstream momentum estimate

t : sluice gate opening

Flow Rate for Closed Method:

Q=AV=tB√(0.9×2 g∆h)=0×0.1524m√¿¿

Hydrostatic Pressure Method for Sluice Gate Closed:

pc=γ ( h2 )=( 9810 Nm3 )( .2032

2 )=996.7 Pa

F=12γ Bh2=( 9810 N

m3 ) 12

( 0.1524m ) (0.2032m )2=30.86N

Static Pressure at Monometer

pi=γ hi = (9810 N) (.19048) = 1868.60 Pa

Force at Monometer

F=∑ piB y i = (1868.60 * 0.1524 * .0127) = 29.69 N

Momentum Theorem Method for Closed

M 1=B y1

2

2+ Q2

gB y12 =

0.1524m(0.2032m)12

2+ 02

gB y12 =3.14×1 0−3m3

M 2=B y2

2

2+ Q 2

gB y22 =

0.1524m(0)12

2+ 02

gB y12 =0

F=γ (M 1−M 2)=( 9810 Nm3 ) (3.146×1 0−3m3−0 )=30.862N

F. Results and Discussion

Head Change Plots

0 2 4 6 8 10 12 14

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Method 1: Head Change (Sluice Gate Closed)

Elevation HeadPiezometric HeadPressure Head

Manometer Number

Mea

sure

d H

ead

(m

)

0 2 4 6 8 10 12 14

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Method 2: Head Change (Sluice Gate Open 0.5")

Elevation HeadPiezometric HeadPressure Head

Manometer Number

Mea

sure

d H

ead

(m

)

0 2 4 6 8 10 12 14

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Method 3: Head Change (Sluice Gate Open 0.75")

Elevation HeadPiezometric HeadPressure Head

Manometer Number

Mea

sure

d H

ead

(m

)

Based on the graphical results, a similar relationship exists for each measured head. The pressure head decreases as the monometer number increases. This makes sense due to the fact that the first monometer is at the deepest level. Theoretically, pressure would be greatest at the bottom due to the weight of the water exerting force. In addition, as the monometer number increases, so does the elevation head. The piezometric head showed minimal change, however it did arrive at a plateau at a certain point as the monometer increases.

According to the results, as the opening of the sluice gate increases, the flow rate increases as well. The results are valid due to the fact that flow rate is dependent on the change of height of the gate. Also, an increase in height allows for a greater area on which the flow is passing through. Therefore, one could say that flow rate Q, is in direct relationship with the height of the sluice gate opening, h.

Summary of Results Table

Data Result Table 4 (Forces N)Method

Experiment No.Hydrostatic Pressure

Force (N)

Actual PressureForce (N)

Momentum EquationForce (N)

1 30.87 29.69 30.8622 27.13 21.78 24.953 26.91 18.76 22.44

Total 84.91 70.23 78.25

Mean 28.30 23.41 26.08

Percentage Difference

Data Result Table (Percent Difference)1: Percent Difference of Hydrostatic

Force and Actual Pressure Force18.90%

2: Percent Difference of Momentum EquationForce and Actual Pressure Force

10.79%

3: Percent Difference of Hydrostatic ForceForce and Momentum Force

8.16%

Out of all three methods, the lab states that the Hydrostatic Method is the most conservative. The results indicate this is true with the hydrostatic method having the highest mean force at 28.3 N. In this method, a triangular pressure distribution is assumed, but this is only accurate for the closed method. According to the results for the closed gate, the resulting forces for all three methods have a small percentage error: 3% between Hydrostatic and Actual Pressure method, and less than 1% between Hydrostatic and Momentum. These 3 results for experiment 1 all had close values. With the gate open, the percentage difference value increases. A reason for this error is because the hydrostatic method is not an accurate method for estimating the force on an open gate. The triangular pressure distribution cannot be assumed when the gate is open. The actual pressure method and momentum equations are a better choice. Some other error can occur, during the experiment an 8-inch elevation is to be maintained and monometer readings can be inaccurate as well. It can be difficult to keep the downstream and upstream levels as steady as possible like stated in the procedures.

G. Conclusions

Overall this lab serves its purpose in calculating forces on a sluice gate by using 3 different methods; hydrostatic, actual and momentum equations. The forces are determined with a closed gate, and open at both .5 and .75 inches. Each method explores a different theory and is useful in accurately calculating forces. A graphical display of the results helps derive relationships between the measured heads and the monometers. These factors are very important in designing sluice gates in the real world such as open channels, water treatment plants and dams.