FEATI UNIVERSITY Helios St., Sta Cruz Manila COLLEGE OF ENGINEERING AND TECHNOLOGY CIVIL ENGINEERING DEPARTMENT
HYDRAULICS LABORATORY MANUAL
BY ENG’R. TOMAS U. GANIRON, JR. June 1994
EXPERIMENT NO. 01
DISCHARGE MEASUREMENT USING A VOLUMETRIC TANK OBJECTIVE: To measure Q which is the rate of discharge or flow from a source in units of volume per unit time. EQUIPMENT: Volumetric tank or container of measurable capacity Stop watch Weighing scale Water source Tape measure FORMULAS: Q1
= total volume (m3/s) elapsed time
where: Q = volume discharge in kg.wt/s M2 =
Weight elapsed time
where: M = mass discharge water Q = M2 P where: P = mass density of liquid = 1 KN/ m3 for water PROCEDURE: A. For Q, 1. 2. 3. 4. 5.
Measure volume of tank/container in m. Turn on flow reservoir or source of steady flow Catch flow into container at same time that stop watch is started. Determine time in seconds to fill tank/container. Repeat at least 2 trials w/ different openings of top/source.
B. For M2 (if weighing scale is available for use) 1. Place container on weighing scale and determine weight of empty container, (W0) in kg.wt. 2. Turn on flow from reservoir or source. 3. Record time that the mass-weight of container and flow reach several values of W1, W2, etc.. DATA AND COMPUTATIONS:
SKETCH:
THEORY/DISCUSSION:
CONCLUSION:
RECOMMENDATION:
EXPERIMENT NO. 02
VENTURI METERS OBJECT: To measure the rate of flow in pipe and to determine the coefficient of discharge Cd. THEORY: A constriction in a stream tube tend to produce an accelerated flow and fall of pressure which is directly related to flow rate and thus is an excellent matter in w/c rate of flow maybe calculated from pressure measurements. The form of Venturi tube is usually a conical nozzle like reducer followed by a more general enlargement to the original size. It is generally a casting consisting of an upstream section w/c is the same size as the pipe, has a bronze lining and contains a piezometer ring for measuring static pressure; a converging conical section; a short cylindrical section containing a piezometer ring and a diffuser in order to minimize head loss. The pressure at the base of meter (section 1) and at the throat (section 2) are obtained by piezometer rings and the pressure difference is usually measured by a differential manometer. The pressure at the upstream section and throat are the actual pressures. The velocities from Bernoulli’s equation are theoretical velocities. If losses are considered in the energy equation, the velocities are then the actual velocities. Now from the principle of continuity, Q = AV, the actual velocity times the actual area of the throat determines the actual discharge. Because of stream lining the flow passage, any contraction beyond the smallest section is eliminated; consequently the coefficient of contraction has a value of unity and the basic discharge equation for the venture meter for incompressible flow is:
Q = CdA2
2gR1 [(So/Si)] – 1
½
1 – (D2/D1)4
where: R1 = gage difference S0 = specific gravity of manometer liquid S = specific gravity of flowing liquid Note, that since the contraction coefficient is unity: hence Cd = CvCc = C1(1) or Cd = Cv where: Cd is the coefficient of discharge
APPARATUS: Hydro-synthetic machine Stop watch Container PROCEDURES: 1. Run the pump to let water flow through the pipe lines. 2. Allow the liquid to collect in a container and note the rise in the liquid surface in a measured time. 3. Read the manometer gage difference. 4. Make five (5) trials. REPORT: 1. Derive the formula for the actual discharge through a venture meter. 2. What is a piezometer and what is its function? 3. What is the purpose of the contriction in the venture meter? 4. How is the pipe line flow measured by a nozzle, orifice and elbow meters? Sketch the longitudinal section and discuss briefly the working principle.
5. Compute the average coefficient of discharge.
DATA:
COMPUTATIONS:
GRAPH:
SKETCH:
DISCUSSION:
CONCLUSION:
REFERENCES:
DATA:
EXPERIMENT NO. 03
AN INVESTIGATION OF DARCY-WEISBACH EQUATION
I. INTRODUCTION: A. Background The flow of fluids through various conduits and elements results in a friction loss. This experiment aims to examine this loss with the use of the Friction Loss Apparatus. B. Statement of the Problem To investigate the validity of the Darcy-Weisbach Equation. C. Objective 1. To determine the head loss using the head loss apparatus 2. to compare the experimental head loss with the theoretical head loss. II. THEORETICAL CONSIDERATIONS: A. Darcy-Weisbach Equation h = f L D
V
2g
where: f = friction factor L = length of pipe, m V = velocity, m/s D = pipe diameter, m g = gravity, m/s
III. EXPERIMENTATION: A. Procedure of Experiment 1. Select the pipe lines to be considered in the experiment. 2. Take note of the pipe diameter involved. 3. Measure the lengths of the pipe involved. 4. Allow the water to flow. 5. Determine the discharge by taking note of the volume of flow and time taken. 6. Repeat for other pipes selected. B. Data Trials Length (m)
Dia. (m)
1 2 3
COMPUTATIONS:
APPARATUS:
Area (m2)
Vd (m3)
t (sec)
Q (m3/s)
V (m/s)
f
h
DISCUSSION:
CONCLUSION:
RECOMMENDATION:
REFERENCES:
EXPERIMENT NO. 04 DISCHARGE MEASUREMENT USING AN ORIFICE OBJECTIVE: To measure discharge through an orifice by: a. Trajectory method b. Direct measurement of jet diameter and velocity at vena contracts by a Pitot tube. PRINCIPLE: An orifice is an opening (usually) circular in the wall of a tank or in a plate normal to the axis of a pipe either an end of pipe or in some intermediate location. An orifice is characterized by the very small relation of wall or plate thickness compared to the size of the opening. Fig. (a) and (b) are standard orifices, (c) and (d) are not standard because the flow through them is affected by the following thickness of plate, roughness of surface and radius of curvature. A jet is a stream issuing from an orifice, nozzle or tube. It is not enclosed by solid boundary walls but surrounded by fluid of the same type, say a gas jet discharging in to a gas or a liquid. A submerged jet is buoyed up by the surrounding fluid and is not directly under the action of gravity. h1 = h3 + V12 2g V1 =
2g (h1-h3)
=
2g (∆H)
V1 = ideal velocity at vena contractu
There the streamlines converge in approaching an orifice, as shown in fig. B, they continue to converge beyond the upstream section of the orifice until they reach the section xy where become parallel. Commonly this section is about USD. From the upstream edge of the opening, where Do ids the diameter of the orifice. The section xy is then the section of minimum area and is called the vena contract. Beyond the vena contract, the streamlines commonly diverge because of frictional effects. The minimum section is referred as a submerged vena contract as it is surrounded by its own fluid. In Fig. A-4, there is no vena contract as the rounded entry to the opening permits of the streamline to gradually converge to the cross-sectional area of the orifice. Jet velocity is defined as the average velocity of the vena contracts. A free liquid to jet will describe a trajectory, a path under the action of gravity. The trajectory is streamline, and if an friction is neglected. Vo = x g 2z
where: x = range z = mass ht.
Coefficients: Coefficient of contraction, Cc = Ajet A orifice or opening Coefficient of velocity, Cv = Vi
V
where: Vi = ideal velocity for no friction Coefficient of discharge, Cd = actual Q ideal Q
APPARATUS: Stop watch Meter stick Rectangular weir Caliper PROCEDURE: 1. Measure orifice area and vena contracts using caliper and orifice area. 2. Determine the (water) height in m. 3. Allow the H2O to flow in volumetric tank. Measure the volume and time as the water reaches the higher depth. 4. With the aid of meter stick, determine the position of the vena contrata (x and y). 5. Compute for the three coefficient of orifice. DATA: Aj Aa Cc H Vt V Cv Vol Time Q Qt x y c Cc (m2) (m2) (m) (m/s) (m/s) (m3) (s) (m3/s) (m3/s) (m) (m)
COMPUTATIONS:
DISCUSSION:
RECOMMENDATION:
DRAWING:
CONCLUSION:
REFERENCE:
EXPERIMENT NO. 05 AN EXPERIMENT ON WEIR APPARATUS
I. INTRODUCTION A. Background of the Study. A weir involves flow of a liquid with a free surface over the top of the plate. It is also an overflow structure built across an open channel for the purpose of measuring the flow. It is commonly used to measure the flow of the water, but their used in measurement of other liquids is increasing. The same principle applies to all liquids, and the fundaqmental formulas based upon these principles are in all respects general. Classification with reference to the shape of the opening through which the liquid flows, weirs maybe rectangular, triangular, trapezoidal, circular, parabolic or any other regular form. The first three forms are most commonly used for measurements of water; the triangular weir is usually best adapted for measurements of other liquids. B. Statement of the Problem. This study aims to associate us with the uses and purposes of weir apparatus. C. Objective of the Study To compare the theoretical discharge, Q with the actual value of Q by the use of weir. APPARATUS: Meter stick Stop watch Weir accessories
PROCEDURE:
1. Start the machine at low voltage, get the discharge and height of water using trapezoidal, triangular and doubly rectangular contracted weir. 2. Tabulate the result. DATA: Types of Weir Trapezoidal Triangular Doubly Rectangular Contracted COMPUTATIONS:
DISCUSSION:
H (m)
t (s)
Actual Q (m3/s)
Theoretical Q (m3/s)
% Error
DRAWING
CONCLUSION:
RECOMMENDATION:
EXPERIMENT NO. 06 LAMINAR AND TURBULENT FLOWS I. INTRODUCTION: A. Background of the Study Hydrokinetics is that branch of hydrology which deals with the study of fluids, mainly water. In motion, it is totally different from hydrostatics both in concept and in principle. In the history of hydraulics, many investigation have been made to determine the laws which govern the flow of fluids in closed conduits. Chezy, in 1775, developed one of the earliest expressions for energy loss in pipes. This and many other empirical formulas, developed from test data, were based on the assumption that energy loss was dependent only on velocity, conduit dimensions, and wall roughness. However, these studies were to be followed by other researches which showed that fluid density and viscosity were also factors to be considered. Included here are the works of Hagen (1839), Poiseuille (1840) and Osborne Reynolds (1883), whose Reynold’s Number will be the main focus of this study. B. Statement of the Problem. This study aims to investigate in its entirely the concept and principle behind the Reynold’s Number through actual experimentation. D. Objective of the Study. 1. To determine the Reynold’s Number of water at any given flow condition. 2. To determine the range of Reynold’s number between laminar and turbulent flow.
II. THEORETICAL CONSIDERATIONS: A. Concepts. In the classification of flow, one must determine whether fluid movement is laminar or turbulent. In laminar flow, the fluid moves in parallel layers with no crosscurrents. Meanwhile, turbulent flow is characterized by pulsatory crosscurrents velocities which result in the formation of a more uniform velocity distribution. However, it is also important to note that turbulent flow experiences greater energy loss than laminar flow. In circular pipes, the maximum velocity for laminar flow is twice the average velocity: whereas for turbulent flow, it is approximately 1.25 times the average velocity.
B. The Reynold’s Number The Reynold’s number (R) is the criterion which distinguishes between laminar and turbulent flow. For circular pipes, flowing full: R= u
dvp
=
dv
v
where: d = diameter of pipe v = average velocity p = density u = viscosity v = kinematic velocity
In pipes, when R is less than or equal to 2,100, the flow is said to be laminar. Turbulent flow, on the other hand, occurs when R is equal to or greater than 3,000. For values R between 2,100 and 3,000, flow is said to be in a transitional condition. In order to better understand the physical significance of the Reynold’s Number. It can be expressed as the ratio of the inertial force to viscous force. Here, the inertial force represents the tendency of a fluid to develop turbulence at boundary irregularities while the viscous force tends to damp out turbulence. D. Derivation of Reynold’s Number Let us suppose that we have a cube of fluid of side d in a fluid flow of velocity V. To accelerate this body requires a force equal to the mass times the acceleration. As measure of the acceleration we take dV/dt V/t V2/d, and the mass equal to Qd2, we obtain an inertial force Fin Qd2V2 The viscous shear forces are proportional to the viscosity, cross-sectional area, and the velocity gradient; that is, Fvis uVd
where Fin
= inertial force
Fvis
= viscous force
III. PROCEDURE: 1. Measure the diameter of the pipe w/ vernier caliper. 2. Dteremine the unit of water in N/m3 and kinematic viscosity include the room temp. at C. 3. Measure height of 10cm, 30cm, 20cm and 40cm. Then allow the water to flow. The value should be adjusted. Take the time required for each height. 4. After gathering the required data, compute for Reynold’s number and determine the flow w/c is laminar and turbulent. Fill the data sheets.
DATA SHEET: Pipe diameter
=
Room temp.
=
Mass density
=
Weight
=
Cross-sectional area of pipe = Kinematic viscosity
Trial No.
Vol. (m3)
=
Time (s)
Q (m3/s)
Velocity (m/s)
Re
Remarks
1 2 3 4
DISCUSSION: Chezy, in 1775, developed one of the earliest expressions of energy loss in pipes. This and many other empirical formulas, developed from test data, were based on the assumption that energy loss was dependent only on velocity, conduit dimensions and wall roughness. However,
these studies were to be followed by other researches which showed that fluid density and viscosity were also factors to be considered. In the classification of flow, one must determine whether fluids move in parallel layers with no crosscurrents. Meanwhile, turbulent flow is characterized by pulsatory crosscurrent velocities w/c result in the formation of a more uniform velocity distribution. Turbulent flow experiences greater energy loss than laminar flow. We only distinguish the classification of flow by getting the Reynold’s number. The formula for Re is the product of the diameter of pipe and the average velocity for viscosity. The result of this formula will identify whether the flow is laminar or turbulent. Reynold’s number less than 2,000 considered as laminar and Reynold’s number greater than 4,000 considered as turbulent flow.
COMPUTATIONS:
APPARATUS:
CONCLUSION:
RECOMMENDATION:
EXPERIMENT NO. 07 ANALYSIS OF PIPE NETWORK OBJECTIVE: To study piping system encountered on water supply distribution system. APPARATUS: Assembly of 8 hydraulic bench. PRINCIPLE: An extension of pipes in parallel is a case frequently encountered in municipal distribution systems, in which the pipe are interconnected so that the flow to a given outlet may come by several different P, as shown in Fig. 8.31. Indeed, it is frequently impossible to tell by inspection which way the flow travels, as in pipe BE. Nevertheless, the flow in any network, however complicated, must satisfy the basic relations of continuity and energy as follows: 1. The flow into any junction must equal the flow out of it. 2. The flow in each pipe must satisfy the pipe-friction laws for flow in single a pipe. 3. The algebraic sum of the head and any closed loop must be zero. Pipe networks are generally too complicated to solve analytically, as was possible in the simpler case of parallel pipes (Sec. 8.26). A practical procedure is a method of successive approximations, introduced by Cross. It consists of the following elements, in order: 1. By careful inspection assume the most reasonable distribution of flow that satisfies condition1. 2. Write condition 2 for each pipe in the form hL = KQn Where K is the constant for each pipe. For example, the standard pipe-friction equation in the form of Fig. (8.62) would yield K = 1/C2 and n = 2 for constant f. The empirical formulas (8.45) and (8.46) are seen to be readily reducible to the desired form. Minor losses within any loop may be included but many losses at the junction points are neglected. 3. To investigate condition 3, compute the algebraic sum of the head loss around each elementary loop, ∑hL = ∑KQn. Consider losses from clockwise flows as positive, counterclockwise negative. Only by good luck will these add to zero on the first trial.
4. Adjust the flow in such loop by a correction, ∆Q, to balance the head in that loop and give ∑KQn 0. The heart of this method lies in the determination of ∆Q. For any pipe we may write, Q = Q0 + ∆Q where Q is the correct discharge and Q0 is the assumed discharge. Then, for each pipe. ∑hL = KQll = K (Q0 + ∆Q)ll = + mon-1∆Q + …) If ∆Q is small compared with Q0, the terms of the series after the second one may be neglected. Now, for a circuit with ∆Q the same for all pipes. ∑hL = KQll = ∑KQno + ∆Q ∑KQn-20 = 0 As the corrections of head loss in all pipes must summed arithmetically, we may solve this equation for Q. ∆Q
=
- ∑ KQno ∑ KnQon-2
∑Lh
=
n∑
hL Qo
as for Eq. (8.63), hL Q = KQn-1. It must be emphasized again that the numerator for Eq. (8.64) is to be summed algebraically, with due account of sign, while the denominator is summed arithmetically. The negative sign in Eq. (8.64) indicates that when there is an excess of hand around n loop in the clockwise direction, the Q must be subtracted from clockwise Qo 5 and added to counterclockwise ones. The reverse is true if there is a deficiency of hand loss around a loop in the clockwise direction. 5. After each circuit is given a first correction, the losses will still not be balance because of the interaction of one circuit upon another (pipes which are common to two circuit receive two independent corrections, one for each circuit). The procedure is repeated., arriving at second correction, and so on, until the correction become negligible. PROCEDURE: 1. Take up the ½, ¾ and 1 inch piping assembly. Open their gate valve. 2. Record reading of manometer simultaneously. 3. Compute their discharge.
DISCUSSION:
DATA:
COMPUTATIONS:
DRAWING:
CONCLUSION:
RECOMMENDATION:
EXPERIMENT NO. 08 OPEN CHANNEL FLOW
DESCRIPTION: I. Definition. Open channel is applied to liquid flow exposed to atmospheric pressure. II. Main types of open channels are: a. Natural streams or rivers b. Artificial canals or flumes c. Sewers, tunnels and pipe lines not flowing full III. Essential properties of uniform flow in open channels are: a. b. c. d.
Uniform depth : d1 = d2 = depth at any section Uniform areas : A1 = A2 = area at any section Uniform velocity : V1 = V2 = velocity at any section Equal slopes of energy gradient of stream bed and water Surface : S = Sd = Sws S = hf = slope of the stream bed L S0 = slope of steam bed Sws = slope of water surface or hydraulic gradient
IV. Formulas: a. Chezy equation (1775) V=C
RS
where: R = hydraulic radius = A P S = slope of energy gradient sin= tanfor small c = coefficient dependent on characteristics of channel, length and time.
b. 3 Ways of finding of C 1. Kutter and Ganguillet equation (1869)
C=
23 + .00155 + 1 s n 1 +_n_ (23 + .00155) R
5
2. Manning equation (1890) V = 1/n R2/3 S1/2 where: C = R1/6 n 3. Bazin equation (1887) C = __87__ 1+m R
m=n restricted for m small artificial channels xerox of table
PROCEDURE: 1. Allow the water to flow in a volumetric tank and measure the discharge by determining the following parameters. L = .50m W = .10m A = .0015m2V = .00075m3
t = .015m t = 10 s
2. As the water flow measure the wetted perimeter of the channel and determine the slope of e.g. and channel are equal. Pw = .035 (2) + .10 S = .015 So = .035/.10
A = .0035m R = .0206m
Note: Roughness coefficient of iron pipe (n) = 0.015 3. Compute the discharge obtained in Procedure 1 and 2 and compare the values. COMPUTATIONS:
CONCLUSION:
RECOMMENDATION:
EXPERIMENT NO. 09 HYDRAULIC JUMP
OBJECTIVES: To analyze water surface profile in a rectangular channel producing a mark discontinuity – the surface characterized by an upward steep slope of the profile broken throughout with violent turbulence and known universally an hydraulic jump. PRINCIPLES: This phenomenon occurs when supercritical flow is reduced to sub-critical. Some situations which produces hydraulic jump are the following: a. when there is a change of slope in the channel. b. When there is a change in width in the channel. c. When uniform flow changes to non-uniform flow due to an obstruction. EQUIPMENT: Tape measure Steady source Rectangular flume PROCEDURE: 1. Measure the depth of upper and lower stream of water as the water flow. d1 = 2.5cm d2 = 15.5cm 2. Determine the width of the channel. 3. Allow the water to flow and determine the discharge of the channel. Measure the following parameters. Volume of the tank = .116m3 time = 112s Q = 1.04 x 10-3m3/s V1 = .4 m/s V2 = .064m3 4. Compute the provide no. of upper stream and lower stream. F1 = .80 F2 = .05
5. Classify what type of flow obtain in upper stream and lower stream. DEFINITION AND FORMULAS: 1. Critical depth – is the depth at which velocity is maximum, V = critical velocity. This occurs at 0.6y to 0.7y. It is also the depth of minimum specific energy for a given flow. Yc = E =
____2____ E 3 y + __V2_ 2g
eq. 1 eq. 2
thus: qmax q
=
gyc3
eq. 3
= volume rate of flow per unit length of rectangular channel = in m/s
2. Super critical flow occurs when __V__ 2g 3. Sub critical flow occurs when __V__ 2g
> <
__Yo__ 2 __Yo__ 2
4. For a rectangular channel & slope 5% Y2 = Y1 2
(-1 +
1 + 8q2 gy12
eq. 4
5. Length of jump – approximated to about 5y2, since this is difficult to determine. DATA: n b Q S1 S2
= = = = =
COMPUTATION AND PROCEDURE: 1. Solve for y01 = normal flow at upper slope flow for rectangular channel. Q = di ko maintindihan Rm = ( _A1_ + __A2_ ) P1 P2 2 S = ( nVm ) R2/3m So = slope 2 PROFILE:
DATA AND COMPUTATIONS:
CONCLUSION:
DISCUSSION:
DRAWING:
CONCLUSION:
RECOMMENDATION:
EXPERIMENT NO. 10 WATER HAMMER OBJECTIVE: To measure water hammer EQUIPMENT: Water source Velocity measuring devices (Pitot tube) Stop watch Caliper PRINCIPLE: Water hammer occurs in liquid-flow pressure systems whenever a valve is suddenly closed. This is an increase in pressure and acts as a pressure wave when velocity of a liquid is decreased abruptly. Three Cases of Study: 1. Ideal case – instantaneous closure (Physically impossible) Tr = 2L Cp Ph = CpV
Tr = time for round trip of pressure wave in L distance
2. Rapid closure Tc < 2L Cp X = tc Cp 2
Tc = time of closure X = distance from intake to point given
3. Slow closure tc > 2L Cp C = di ko mawawaan C Bv D t Ev Cp
= celerity of pressure wave in liquid = 1440m/s for water = Bulk modulus of liquid = mass density of liquid = diameter of elastic pipe = thickness of elastic pipe = elasticity of elastic pipe = pressure wave in elastic pipe = 600 1200m/s 1440m/s
B. Vary Q and tc for partial closure COMPUTATIONS:
Problems Give three method of protecting pipe from effects of high-water hammer pressure.
DATA SHEET:
PROCEDURE:
DISCUSSION:
DRAWING:
CONCLUSION:
RECOMMENDATION:
