RepublicofIraq MinistryofHigherEducation andscientificresearch UniversityofTechnology- Electromechanical Department - 2014 1436
Experiment No. 1 Calibration of Bourdon Gauge Description: Figure (1) shows the photography and schematic of bourdon gauge device, this device consist of: Figure (1) shows the photography and schematic of bourdon gauge device. 1. Piston 2. Weights Weights may be added to the piston so that a number of predetermined pressures may be set up within the cylinder. [2]
3. Baseboard The cylinder is mounted on a baseboard which is supported on leveling screws and fitted with a spirit level. 4. Gauge Connection The gauge under test is linked to the cylinder connection by a flexible tube. 5. Waste Water Leakage of water past the piston is taken to waste through connection to a second flexible tube. This tube is connected to a tapping which is drilled into the cylinder and is opposite a n annular recess in the cylinder. 6. Technical Data The following dimensions from the equipment are used in the appropriate Calculations. Required these values may be checked as part of the experimental procedure and replaced with your own measurements. Mass of piston Diameter of piston M p = 498 g D = 0.05767 m [3]
Nomenclature: Column Heading Units Nom. Type Description Mass of Piston g M p Measured Given piston mass Diameter of Piston m D Measured Given piston diameter Area of Piston m 2 A Measured A = D 4 Mass of Load Kg M w Measured Weights applied to the calibrator. Total Mass Kg M Measured = + Gauge Reading Cylinder Pressure Absolute Gauge Error %o Gauge Error KN/m2 G Measured The reading taken from the Bourdon Gauge. KN/m2 P Measured = KN/m2 E A Measured = % E A Measured % = 100 Objective: 1. To calibrate a pressure gauge Bourdon type in to determine the gauge error. 2. To determine the measurement errors in the reference pressure source used for calibration. [4]
Method: To calibrate a pressure gauge by applying predetermined pressures generated by loading weights on to a piston of known cross-sectional area (a "dead-weight calibrator"). Equipment Required: In order to complete the demonstration of the Bernoulli apparatus we need a number of pieces of equipment. The Hydraulics Bench. The Dead Weight Calibrator. Weights. Weigh-balance. Pressure gauge. Filling tube or Measuring Cylinder. Theory: The use of the piston and weights with the cylinder generates reference pressure (P): = And Where : = F is the force applied to the liquid in the calibrator cylinder, M is the total mass (including that of the piston), A is the area of piston. The area of the piston can be expressed in terms of its diameter, D, as: [5]
Readings and Results:- = 4 All readings should be tabulated as follows: Mass of Piston (M p ) Kg Diameter of Piston (D) m Area of Piston (A) m 2 Mass of Load (M w ) Kg Total Mass (M) Kg Gauge Reading(G) KN/m Cylinder Pressure (P) KN/m 2 Absolute Gauge Error KN/m 2 % Gauge Error Plot a graph of gauge reading against absolute and % gauge error. Conclusions: Comment on the accuracy of the gauge. Comment on the size of gauge errors in relation to the errors in the reference pressure measurements. Is the relative height between the dead-weight calibrator and the gauge important in the calib Discussion:- 1- What is the effect of rotation of piston on gage reading? 2- Will you obtain the same reading if you change the liquid? 3- Explain the effect of Hysteresis on the reading of the gage? 4- List the causes of reduces the percentage of error, when the pressure increases? [6]
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Experiment No. 2 Convergent-Divergent Tube Objective:- To investigated the validity of the Bernoulli equation when applied to the steady flow of water in a tapered duct. Method:- To measure flow rates and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. Equipment:- In order to complete the demonstration of the Bernoulli apparatus we need a number of pieces of equipment. 1. The Hydraulics Bench which allows us to measure flow by timed volume collection. 2. The Bernoulli's Apparatus Test Equipment. [8]
3. A stopwatch for timing the flow measurement. As shown in figure below. Technical Data:- The following dimensions from the equipment are used in the appropriate calculations. If required these values may be checked as part of the experimental procedure and replaced with your own measurements. The dimensions of the tube are detailed below:- Tapping Position Manometer Legend Diameter (mm) A h 1 25.0 B h 2 13.9 C h 3 11.8 D h 4 10.7 E h 5 10.0 F h 6 25.0 [9]
Nomenclature:- Column Heading Volume collected Time to collect Units Nom. Type Description m 3 V measured Taken from scale on hydraulics bench The volume collected is measured in liters. Convert to cubic meters for the calculations (divide reading by 1000). s t measured Time taken to collect the known Volume of water in the hydraulics bench. Flow rate m 3 /s calculated q v =V/t =volume/time to collect. Manometer h x given Manometer identication labels Legend Distance into duct m given Position of manometer tapping given as distance from the datum at tapping h1.see test section dimensions. Area of duct m 2 A given The areas of the duct at each tapping see test section dimension. Static head m h calculated Measured value from the appropriate manometer. The manometer readings are taken in (mm) water. Convert to (m) water for calculation? velocity m/s v calculated Velocity of uid in duct= Qv/A Dynamic head m calculated V 2 /2g see theory Total head m h o calculated h+v 2 /2g see theory Distance into m measured Position of the total head probe duct Probe reading h 8 m from the datum at tapping h 1. measured Measured value taken from h 8.this is head recoded from the total head probe. [10]
Theory - The Bernoulli Equation The Bernoulli equation represents the conservation of mechanical energy I for a steady, incompressible, frictionless ow:- + Where + = + + p = static pressure detected at a side hole, v = uid velocity. z = vertical elevation of the uid, hence, z 1 = z 2 for a horizontal tube. The equation may be derived from the Euler Equations b integration. it may also be derived from energy conservation principles. Derivation of the Bernoulli Equation is beyond the scope of this theory. Other Forms of the Bernoulli Equation:- Hence: If the tube is horizontal, the difference in height can be disregarded + 2 = + 2 With the apparatus, the static pressure head p, is measured using a manometer directly from a side hole pressure tapping. The manometer actually measures the static pressure head, h, in meters which is related to p using the relationship: =/ [11]
This allows the Bernoulli equation to be written in a revised form, i.e: + + The velocity related portion of the total pressure head is called the dynamic pressure head. Total Pressure Head The total pressure head, h, can be measured from a probe with an end hole facing in to the ow such that it brings the flow to rest locally at the probe end. Thus, h = h + =. (meters) and, from the Bemoulli equation, it follows, that Velocity Measurement The velocity of the ow is measured by measuring the volume of the ow, over a time period, t. This gives the rate of volume ow as: Q v = which in turn gives the velocity of ow through a dened area A,ie. V= Continuity Equation:- For an incompressible uid, conservation of mass requires that volume is also conserved, A 1 v 1, =A 2 v 2 (m 3 /s) [12]
Procedure - Equipment Set Up:- Level the apparatus Set up the Bernoulli equation apparatus on the hydraulic bench so that its base is horizontal; this is necessary for accurate height measurement from I the manometers. Set the direction of the test section. Ensure that the test-section has the 14 tapered section CONVERGING in the direction of ow. If you need to reverse the test-section, the total pressure head probe must be withdrawn before releasing the mounting couplings. Connect the water inlet and outlet. Ensure that the rig outow tube is positioned above the volumetric tank, in order to facilitate timed volume collections. Connect the rig inlet to the bench ow supply; close the bench valve and the apparatus ow control 1 valve and start the pump. Gradually open the bench valve to full the test rig with water. Bleeding the manometers In order to bleed air from pressure tapping points and manometers, close I both the bench valve, the rig ow control valve and open the air bleed screw and remove the cap from the adjacent air valve. Connect a length of small bore tubing from the air valve to the volumetric tank. Now, open the bench valve and allow ow through the manometers to purge all air from them; then, tighten the air bleed screw and partly open the bench valve and test rig ow control valve. Next, open the air bleed screw slightly to allow air to enter the top of the manometers (you [13]
may need to adjust both valves in order to achieve this); re-lighten the screw when the manometer levels reach a convenient height. The maximum volume ow rate will be determined by the need to have the maximum (hl) and minimum manometer readings both on scale. If required, the manometer levels can be adjusted further by using the air bleed screw and the hand pump supplied. The air bleed screw controls the air ow through the air valve, so, when using the hand pump, the bleed screw must be open. To retain the hand pump pressure in the system, the screw must be closed after pumping. Procedure - Taking a Set of Results:- Readings should be taken at 3 flow rates. Finally, you may reverse the test section in order to see the effects of a more rapid converging section. Setting the flow rate. Take the rst set of readings at the maximum ow rate, then reduce the volume flow rate to give the h1- h5 head difference of about 50 mm. Finally repeat the whole process for one further ow rate, set to give the difference approximately half way between that obtained in the above two tests. Reading the static head Take readings of the h 1 h 5 ; manometers when the levels have steadied. Ensure that the total pressure probe is retracted from the test-section. [14]
Timed volume collection You should carry out a timed volume collection, using the volumetric tank, in order to determine the volume ow rate. This is achieved by closing the ball valve and measuring (with a stopwatch) the time taken to accumulate a known volume of uid in the tank, which is read from the sight glass. You should collect uid for at least one minute to minimize timing errors. Again the total pressure probe should be retracted from the test-section during these measurements. If not using the Fl-l5-301 software, enter the test results into the data entry form, and repeat this measurement twice to check for repeatability. If using the software, perform the collection as described in the walkthrough presentation. Reading the total pressure head distribution Measure the total pressure head distribution by traversing the total pressure probe along the length of the test section. The datum line is the side hole pressure tapping associated with the manometer hi. A suitable starting point is 1 cm upstream of the beginning of the 14 tapered section and measurements should be made at l cm intervals along the test-section length until the end of the divergent (2l ) section. Reversing the test section Ensure that the total pressure probe is fully withdrawn from the test-section (but not pulled out of its guide in the downstream coupling). Unscrew the two couplings, remove the test-section and reverse it then re-assemble by tightening the coupling. [15]
Readings and Results -: Volume Time to Flow Distance Area Static Velocity Dynamic Total collected collect rate Qv into of duct head h v head head V (m 3 ) t(sec.) (m3/s) duct (m) A (m 2 ) (m) (m/s) (m) ho (m) h 1 0.00 h 2 0.0603 h 3 0.0687 h 4 0.0732 h 5 0.0811 h 6 0.1415 Discussion:- Comment on the validity of the Bernoulli equation for convergent ow divergent ow State clearly the assumptions made in deriving the Bemoulli equation and justifications for all your comments. Comparison of the total heads obtained by the two methods you have carried out. [16]
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Experiment No. 3 Flow through an orice apparatus Objective:- 1. To determine the coefficient of discharge, velocity and contraction of a small orice. 2. Determine the losses in head, ow rate, and energy. Method:- - Determination of coefficient of discharge by measurement of volume flow rate from the orice. Determination of coefficient of velocity by measurement of total head at the orice using pitot tube. Determination of coefficient of contraction by measurement of jet diameter and the vena contract diameter. Description :- The orice Discharge accessory consist of a cylindrical tank which has a hole in the base to accept one of ve orices, each with a different prole. The exible inlet pipe is connected to the quick release connector on the hydraulics bench. Water is delivered to the tank via an inlet pipe which is adjustable in height and tted with a diffuser to reduce disturbances in the tank. An overow pipe maintains the water at a xed level in the tank and excess water is returned to the sump tank of the hydraulics bench as shown in the figure. [18]
An traverse assembly mounted beneath the base of the tank enables a pitot tube to be positioned anywhere in the jet of water. Attached to the pitot is a ne Wire which can be traversed a cross the jet to measure the diameter of the jet at the venacontract and so determine the contraction coefficient. The traverse assembly in corporate a graduated knob which moves the pitot tube a distance of l mm for each full rotation of the knob. Each graduation on the knob corresponds to a movement of 0.1mm. The pitot tube and a tapping in the base of the tank are connected to monometer tubes adjacent to the tank. These allow the head over the orice and the total head of jet to be measured and compared. The volumetric ow rate of the water discharging from the orice on test can be determined using the volumetric tank on the hydraulics bench. [19]
The different sharp edged of orifice plate shown in the figure below: Theory:- Determination of Coefficients with constant head outow:- From the application of Bernoulli's Equation (Conservation of mechanical energy for a steady, incompressible, frictionless ow ): The ideal orifice outflow velocity at the jet vena contract at (narrowest diameter) V 0 = 2 Where h is the height of fluid above the orifice. The theoretical ow rate is Q t = V 0 A 0 The actual velocity is V = C V 2 C V is the coefficient of velocity, which allows for the effects of viscosity [20]
and, therefore C V < 1 For the pitot tube h c = V=2 Hence, C v = The actual ow rate of the jet is dened as: Q act = A c v Where Ac is the cross- sectional area of the vena contracta given by: A c = C c A 0 Where C c = = A 0 is the orice area and C c is the coefficient of contraction and therefore, C c < 1 Hence Q act = C c A o C v 2 But C d = C c * C v So finally, Q act = C d A o 2 If C d is assumed to be constant, then a graph of Qt plotted against will be linear and the slop, S = C d A 0 2 The losses as head: h L = h o _ h c [21]
The losses in ow rate: Q L = Q th _ Q act The losses in energy is: P lost = Q L h L Procedure- Equipment set up:- Position the apparatus across the channel on the top of the hydraulic bench and level it using the adjustable feet and the spirit level on the base connect the exible in let pipe to the hydraulics bench snop connector in the top channel. Place the end of the overow tube directly in to the hydraulics bench overflow, and adjust the inlet pipe to the approximate level of the head required for the experiment. Turn on the pump and open the bench valve gradually. As the Water level rises in the reservoir towards the top of the overow tube. The bench valve to give a water level of 2 to 3 mm above the over ow level, with the end of inlet tube fully submerged. This will ensure a constant head produce a steady flow through the orice. [22]
Processing Results:- All reading should be tabulated as follows: Orifice Dia. (m) Vena Contracta Dia. (m) Orifice Head (m) Pitot Head (m) Volume (m 3 ) Time (s) Flowrate (m 3 /s) C v C c C d Discussion:- - Is it justialble to assume that C d is Constant over the range of steady ow tested? - Why are the C d values signicantly less than 1.0? - Comparing the C d value for the steady and falling head tests, which value is likely to be more reliable? [23]
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Experimental No (4) Objective:- Discharge over weirs The purpose of the experiment: 1- Calculate the rate of ow through a rectangular gap. 2- Finding coefficient of discharge. 3- Calculate the loss of the energy while water passes the gap. Equipment:- Figure (1) shows the outline of the device use in this exp. Figure (1) discharge over weirs [25]
The experiment theory:- We take two points showing the water molecules uidity. Point (1) before the gap, point (2) at the vertical axis of the middle of the gap, by neglecting the loss of the energy and applying the rule of Bernoulli between two environments (1) and (2) + 2 + = + 2 + Since that the area of the tank section is larger than the area of gap section. We can neglect water motion in point (1). And since point (1) is open to the atmosphere which means (P 1 =0). And also we can assume that the pressure equals to the atmospheric pressure + = = u 2 = The theoretical speed of the water falling over the gap. The area of the slice at the depth dh is ( da=bdh) where b= the hole width. Then, [26]
dq= u z bdh = 2. with integration we can calculate the theoretical ow rate through the gap Q th = 2. Q th = 2. (1) Notice that there is at retraction in the water bundle while it passes through the gap. The retraction occurs with the vertical direction from the Top and the bottom of the sharp end. Also there is a retraction occurs in the bundle with the horizontal direction. Now we can calculate the real water ow by the tank weight Q act = (2) C d = (3) Q act = C d Q th = C d. 2. (4) [27]
Working steps:- 1- Leveling device with the horizontal situation 2- We operate the pump and open the processing value to fill the tank with Water until the water begins to full on the weir 3- We close the water supply value. Allow the excess water to fall until its level equals with the level of the weir lower edge 4- Nut is rotated to move the hook until the applicability of its top with water level consider it the zero readings of the device. 5- Now we open the supplying valve so that water passes over the weir, and measure the total pressure column (H). Then we calculate the spent time by collecting a certain amount of water tank. We open a larger gap in the valve than the rst reading to increase the ow and measure the reading eight times by gradually increase the ow. b=30 mm H=Reading of martin m= mass of water t= time H(m) M(kg) T(s) Log h Log Q act Q th (m 3 /s) Q act (m 3 /s) C d [28]
And also the mean value of (C d ) can calculated from the Figure by using the relationship between (log H) and (log Q act ) The equation (4 ) is wrote as follows: Q act = KH n And take a logarithm to each side of this equation. Log( Q act) = log(k) + n log(h) K = C d 2. C d = From this sketch we can specication the value (n) which means the slope, and (log K) means the vertical distance for the cutting part. [29]
Discussion:- 1- Discuses the value Cd that obtained from gure (log Q act ) (log H) and compare them with those from table. 2- Plot the relationship between Q act.h 3- Compare between value of Cd which is obtained for weirs with the applied values for venturi tube and hole. 4-" give a conclusion for the relationship between'(log Q act )(l0g H)? Is the values of (n) (k) exist with the theoretical values. [30]
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Object:- Experiment No. 5 Impact of Jet 1. Measure the momentum of water fountain clashes with a flat or curved Plate (hemispherical). 2. Compare this force with the rate momentum after and before clash. Equipment:- Figure (1) shows the outline of the device use, consists of transparent glass cylinder ( s ),put in the middle a tube with a jet at the end allows the water to come out of t in the form of a fountain clashes with the plate attached with a holder, the holder attached with the arm that is hanged in the rotation center and free from the other edge. The arm is balanced with the horizontal when the mass is(m)at the zero mark on the arm, by rotating it at the end of the spring until it touches the guide balance attached the arm with the surface of the cylinder without pushing it, when you move the mass with a distance (x) the balance arm deviates to the lower to put the guide back we pump the water from the processing system to come out of the jet in the form of fountain, we can control the water by a valve until the strengthening of the balance arm. [32]
Figire (1) [33]
Theory of experience:- The momentum equation for fixed blade with assumptions : - Steady - Incompressible - Frictionless F = Q(V V ) Then, F = Q(U COS U COS )(1) According to Newton's third law (For every action, there is an equal and opposite reaction) = = ( ) Assuming that there are no losses on the surface and the surface is open(open system) And the jetting is vertical =0 U 1 = U 2 = ()(2) To account the speed (U) by using Bernoulli's equation. U 1 =U 2-2gs (3) (s) is the distance between the jet and the surface of the blade Notice:- 1. Flat plate = 90 [34]
2. Hemispherical plate = 180 Way of Working:- 1- Put the device in a setting situation that the arm is in a balanced situation. 2- Make the water ow through the supplying water and put the jet towards the central of the plate by adjusting the springs of the base. 3- Change the flow then the weight place until it balance. 4- Took a series of readings with an equal increasing of the weight place. 5- Return the steps (1-4) for each place. Readings and Results:- S=37mm, L=15.25 Cm, d=l0cm R N U m/s U m/s X m Q m/s T Sec [35]
Discussion:- l. plot the relationship between R and Q for each type of surface plate. 2. Plot the relationship between R and X for each type of surface plate. 3. Discuss the relationship between F and S. 4. Explain from Bernoulli equation that U=U and are those values are equals I J or not. 5. At any angle the force will be maximum? Explain this from the mathematical equations. [36]
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