Flow Between Two Reservoirs

Dept of Civil Engineering
University of Texas at Austin

Prepared by Ferdinand Hellweger, David R. Maidment,and Brian Adams

Table of Contents


Java Applets are small programs that can present a physical situation and let you manipulate the components of that situation so as to see the effect on its behavior. In this case, a fluid flow system between two reservoirs is presented in an applet called Visiflow, and the user has a number of options about the connection between the reservoirs, including changing pipe diameters, installing pumps, changing the level of the water in the two reservoirs, adding valves and turbines, and changing the pipe roughness. Once a particular configuration is chosen, the user can execute the solution and update the flow through the system and the hydraulic and energy grade lines between the two reservoirs.

Goals of the Exercise

Computer and Data Requirements

This exercise can be executed on any computer running a world wide web browser which is capable of executing Java Applets (Netscape 2.0 or higher). It does not require an external data file. Get the Applet by clicking on:

The web address for this applet is:

When you first load the Visiflow Applet, you will be presented with a view that looks like this. If you don't get any picture of the two reservoirs, this means that you don't have a web browser capable of viewing Java Applets or possibly that your computer system is located within a security system which does not allow entry of Java Applets from outside the local network.


1. Get Acquainted with Visiflow

The reservoirs are located 60m apart and have water levels which can be altered from 0 to 30m elevation on either side.

(a) The Data Box

The flow system shown has two reservoirs whose elevations are shown at the bottom of the Data Box, the left reservoir being at 30m and the right reservoir at 20m. These levels can be changed by clicking on the reservoir surface and dragging them up and down. As you do so, you'll see the discharge between the two reservoirs alter. Initially, the discharge is 89 liters per second. If you lower the left reservoir level the discharge goes down; if you raise it, the discharge goes up. And conversely for the right reservoir. The red line in the diagram is the EGL or Energy Grade Line, which measures the total head of the system at any point, and the blue line beneath it is the HGL or Hydraulic Grade Line, which measures the pressure and elevation head at each point. The maximum and minimum elevations of these lines are shown in the center of the data box, initially as EGL 30/12 and HGL 30/6, indicating that in the left reservoir, the Energy and Hydraulic Grade lines are both at the water surface elevation (30m), and then they decline as energy losses consume head to minimum values of 12 for the EGL and 6 for the HGL, respectively, in this initial example.

(b) The Pipes

If you click on a pipe, you'll see it highlighted in yellow and its parameters shown in the boxes below the diagram. The pipe initially highlighted has a diameter of 10 cm, a length of 10m and a Darcy-Wiesbach friction factor of 0.025. The values in the clear boxes can be altered by the user (diameter and friction factor), while the value in the grey box is determined by the system from the diagram. If you click on other pipes, you can read off their diameter, length and friction factor. Strictly speaking, the friction factor is a function of the velocity and discharge through the pipe, but it is here set to a fixed value to simplify the calculations.

(c)The Fittings

There are four kinds of fittings that can be inserted into the system: a pump, joint, valve, and a turbine. You can insert a fitting by clicking on it and dragging it into position on the pipe system. You remove a fitting by dragging it and putting it into the trash box at the bottom of the fittings list. The applet will adjust the lengths of the pipes between the fittings automatically.

Pumps and Turbines
A pump or a turbine characterized by its head alone. In a more complete analysis of this system, the pump or turbine head would vary according to the discharge through the system but it is here held fixed to simplify the calculations. Pumps supply head to the system, turbines remove it.

Joints and Valves
A joint is characterized by a loss coefficient which is the factor K multiplying the velocity head at that location to give the minor loss associated with the joint between two pipes, or at the entrance or exit to the pipe system. A valve is likewise characterised by a loss coefficient applied to the velocity head. This coefficient can be changed by the user to values of perhaps 1 or 10 or 100 or 1000 representing differing degrees of loss of head as the flow passes through the valve.

Ok, you're ready to run the Applet now!

2. Analysis of Flow Systems

(a) Flow without pumps or minor losses

Lets simplify the system by deleting all the fittings between the reservoirs, and setting the head loss coefficients at the entrance and the exit to 0. Get rid of the pump and the two junctions located on the pipe between the reservoirs by dragging them to the trash box. The screen flickers a bit when you do this but that is because it refreshes itself while you are doing the drag operation. Click on the junction at the entrance and exit and set the loss coefficients to 0 (the default value is 0.5). The only head loss is now the friction loss in the 60m of 20 pipe between the reservoirs. In this situation, the discharge can be found by writing the energy equation between the surfaces of the two reservoirs as:

The value of 160.7 liters per second determined from this computation is the essentially the same as that found in the data box of the Visiflow Applet for these conditions, except that the value shown in the data box is only the integer part of the discharge.

(b) Adding Entrance and Exit Losses

Click on the entrance junction and set the loss coefficient equal to 0.5 (a square-edged entrance) and on the exit junction and set the loss coefficient equal to 1.0 (the velocity head is dissapated as the flow discharges into the outlet reservoir). The flow drops to 146 liters per second to reflect the additional losses. Notice how the energy grade line now drops below the level of reservoir 1 as the flow enters the pipe and the hydraulic grade line on the reservoir 2 runs right into the water surface, indicating that the velocity head is all dissapated as the flow discharges into reservoir 2. The computations can be checked by the following procedure.

(c) Changing the Reservoir Levels

Drag the level of the left reservoir down to 20m and raise the level of the right reservoir to 30m. Click on the entrance and exit junctions and set the values to 0.5 and 1.0, respectively. Here is the same flow system that you just analyzed with the flow going in the opposite direction. You may find that the flow doesn't quite come out to 146 liters per second and if so, make some minor adjustments to the reservoir levels so that the results come out ok.

(d) Adding a Pump

Add a pump with a head of 10m by dragging a pump symbol from the Fittings Box and drop it near the center of the pipe. the discharge is increased to 207 liters per second and the hydraulic and energy grade lines reflect the increase in head at the pump. The discharge computation can be verified as follows.

(e) Changing the Pipe Diameter

Suppose now that we change the diameter of the pipe to the right of the pump from 20cm to 10cm. The resulting discharge drops to 52 liters per second, reflecting the high energy losses in the smaller pipe. The entrance and exit losses now have to be calculated with the corresponding velocities, that is, the velocity in the 20cm pipe for the entrance loss and the velocity in the 10 cm pipe for the exit loss. Notice how there is relatively little head lost in the 20cm pipe and nearly all the energy is dissapated in the 10cm pipe. This occurs because as shown by Eq. (3), the head losses are inversely proportional to the fifth power of the diameter for friction losses in pipes, and inversely proportional to the fourth power of the diameter for minor losses.

(f) Adding a Valve

Valves are added on the outlet side of pumps to control the flow. Here a valve with a loss coefficient of 5 velocity heads reduces the flow from 52 liters per second to 41 liters per second. The calculations can be verified in the same manner as that used previously, by adding the minor loss in the valve to the losses on the right hand side of the energy equation.

Ok! Now you are ready to design a pump and pipe system!!

3. Design Problems

(a) Pump and Valve

Design a pump and pipe system which will convey 200 liters per second of water between two reservoirs whose difference in elevation is 15m using 20cm pipe having a loss coefficient of 0.025. What pump head should be used? If a valve is installed on the outlet side of the pump to control the flow, what loss coefficient should the valve have? What is the power imparted to the flow by the pump (Kw). Note that you need to drag the elevation of the right hand reservoir down to 15m to achieve a 15m difference in elevation between the two reservoirs.

To be turned in: the value of the pump head and valve loss coefficient needed to have a flow of 200 liters per second. Verify the results of the applet calculation by determining the discharge by hand using the methods shown in the previous examples. What power in kW is supplied to the fluid by the pump?

(b) Relationship between Pipe Diameter and Discharge

Reload the applet so that the levels are restored to 30m on the left hand side, and 20m on the right hand side. Install a pump supplying 10m of head at the beginning of the pipe, and change the diameter of the pipe in increments of 5cm beginning at 5cm and ending at 30cm diameter. Note the discharge in the pipe for each diameter.

To be turned in: a graph relating the discharge to the pipe diameter.

(c) Cavitation

Cavitation in pumps occurs when the pressure on the inlet side of the pump falls too low. In this case, a negative pressure head of about 7m is the safe maximum for preventing cavitation. For the conditions in Problem 2, determine what the maximum pipe diameter and discharge through the pump that can occur without inducing pump cavitation. The elevation of the pump is 10m and the negative pressure head on the pump is measured by the difference between the pump elevation (z) and the minimum elevation of the hydraulic grade line (p/gamma = z - h). In the example shown above, the minimum piezometric head is h = 7m, so the negative pressure head on the inlet side of the pump is p/gamma = 7-10 = -3m. This corresponds to a suction pressure of p = -3 * 9.81 kPa = 29.4 kPa or about 1/3 of an atmosphere.

To be turned in: the limiting pipe diameter for cavitation. What is the inlet pressure at the pump for this flow condition?

4. Be Creative!!

Develop a pump and pipeline design that addresses a particular set of physical conditions of your own devising.

To be turned in: a brief description of your pump and pipe design. Draw a diagram showing the layout of the system, specify the dimensions of its components. Specify the discharge through the system and the pump head and power required..

Ok, you're done!

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