Floating fountain design study

Floating fountain design study

Buoyancy, stability, bracing and facilities in lakes and water areas

The floating fountain allows the deployment of display equipment in areas where it is difficult to implement a fixed base or where the water level changes. In this system, the set of nozzles and equipment are moved along with the water level; But the horizontal position, the balance of the structure and its connection with the shore must be controlled.

Designing such a complex, in addition to fountain calculations, requires knowledge of the behavior of the floating structure. Increasing the weight of a lamp, changing the location of the pump or shortening the free path of the cable can affect the performance of the whole set.

This chapter examines a hypothetical example to illustrate basic calculations. The numbers are not actual GSO product or project specifications and must be supplemented with equipment drawings, watershed conditions, and specialized calculations for executive selection.

47–1. Selection of the floating system and its application limits

The choice between fixed and floating structures should be made based on water depth, level changes, bed material, the possibility of implementing the foundation and the repair method.

In the floating system, the approximate constant position of the nozzle relative to the water surface is an important advantage; Especially for nozzles whose spraying quality depends on the depth of installation. Conversely, wind, waves, harness tension and load shifting can change the alignment or direction of nozzles.

In the introduction of floating packages, the GSO website mentions their use in deep areas with changes in level. Also, on the same page, the services performed for Mellat Park's fountain, including lighting and mechanical, control and electrical equipment renovation, have been introduced. GSO floating packages and projects ^[310]

To make an initial decision, four things should be clear:

• The permissible range of movement of the collection on water;

• The lowest and highest operating balance;

• Power supply and control path;

• Method of transferring the collection to the repair place.

47–2. Location information and sample specifications

The hypothetical project of this chapter is located in an artificial urban lake with service access from the shore. Public access to the fountain structure is not foreseen.

The dimensions of the frame do not determine the area of the traversable deck. If the presence of a technician on the complex is necessary, the level of access and its capacity must be designed separately.

Before the final placement, it is necessary to take the depth, check the sediment, identify the underwater facilities, the condition of the bed seal cover and the possible routes of the boat.

Figure note from the source manuscript

Figure 1-47: Conceptual plan of the floating system

Four-meter frame, four buoyancy chambers, nozzle groups, pump location, proposed harness connection points and cable route are displayed. The permitted movement range of the collection and the route of its transfer to the beach should also be clear. Subtitle: "Educational make-up; The number and position of restraints depends on the design of the place.

47–3. Preparation of crime table

Calculation of buoyancy should begin with a list of the mass of all components whose load is transferred to the floats.

The temporary load of 200 kg is the assumption of the analysis and is not considered as the permission for the presence of people on the structure.

In the final version of the table, the coordinates of the center of mass of each component must also be recorded. Two sets of equal mass may have completely different stability if the location of the equipment is different.

Cable tension and harnesses, hydrodynamic forces and splash reaction should also be checked under the relevant loading modes; These forces are not hidden in the constant mass table.

47–4. Basic calculation of buoyancy

The buoyant force is obtained from the following relationship:

$F_B=\rho g{V}_{displaced}$

For simple vertical equilibrium, neglecting other vertical forces:

$V_{required}=\frac{m}{\rho }$

At constant mass:

$V_{required,normal}=\frac{1000}{1000}=1.00m^3$

In hypothetical repair mode with off pumps:

$V_{required,service}=\frac{1200}{1000}=1.20m^3$

Full displacement volume of four compartments:

$V_{float,total}=4\times 0.6=2.4m^3$

Therefore, in the simple model of repair mode:

$\frac{V_{required}}{V_{float,total}}=\frac{1.2}{2.4}=0.50$

That is, the required displacement volume is equivalent to 50% of the full volumetric capacity of the chambers.

This result does not mean the exact sinking of half the height of the floats; The relationship between the volume and the water inlet depends on their geometric shape. Also, residual volume alone is not a safety acceptance criterion. The distance of sensitive points to the water surface, balance, wave and damage condition should be checked.

47–5. Stability and load transfer effect

Buoyancy shows how well the assembly supports its weight. Stability determines whether it has sufficient tendency to return to equilibrium after tilting.

The position of the center of mass, the shape and distance of the floats and their cross section at the water level are effective in this behavior. The guidelines for the stability of the vessels also emphasize the role of the center of mass, the buoyancy force and the free distance to the water; The application of these principles does not mean the automatic application of marine vessel regulations to the fountain. Sustainability Guide from British Maritime Organization ^[311]

To illustrate the effect of load displacement, suppose a temporary load of 200 kg is moved from the middle axis to a distance of 1.5 m:

$M_{heel}=mge$

$M_{heel}=200\times 9.81\times 1.5=2943Nm$

This torque should be compared with the restoring power of the structure. Without the geometry of the floats and the center of mass, it is not possible to declare the angle of tilt or the suitability of the design.

In the detailed design, at least the following modes are checked:

• symmetrical and asymmetrical loading;

• moving equipment during repair;

• asymmetric activity of water groups;

• The effect of wind, wave and tension of restraints;

• Water entering a compartment or water accumulation on parts of the structure.

Figure note from the source manuscript

Figure 2–47: Comparison of buoyancy and stability

Draw two sections of a set with the same buoyancy volume: one with the load in the center and the other with the load transferred to the side. Determine the center of mass, water level and torque direction. Display the tilting angle schematically without numerical value.

47–6. Check for damage to a compartment

If, in a simple check, the buoyancy capacity of one of the four compartments is completely lost, the capacity of the remaining three compartments is equal to:

$V_{remaining}=3\times 0.6=1.8m^3$

The ratio of the required volume for a mass of 1200 kg to this capacity:

$\frac{1.2}{1.8}=0.667$

In terms of total volume, the three compartments still have more carrying capacity than necessary; But the distribution of buoyancy force has become asymmetric. A corner may go down and equipment or water entry points may be below the surface.

Therefore, this calculation is not a verification of the failure tolerance of an enclosure. Damage analysis should take into account the actual shape, location of the failed chamber, water ingress, and change in stability.

The independence of the chambers, the possibility of detecting leaks and the ability to replace each part should be included in the construction specifications.

47–7. Injection calculations and pump power

Flow rate of each group of four:

$Q_{group}=4\times 2.5=10m^3/h$

The total discharge of six groups:

$Q_{total}=6\times 10=60m^3/h$

For educational estimation, we assume the total head of each circuit is 14 meters and the total efficiency of electricity to water is 0.60:

$P_{electric}=\frac{\rho gQH}{\eta }$

$P_{total}=\frac{1000\times 9.81\times (60/3600)\times 14}{0.60}=3815W$

Therefore, the estimated input power of the pumps at the hypothetical working point:

$P_{total}\approx 3.82kW$

This result depends on the sameness of the head and the hypothetical efficiency of the groups. The final selection of motor and pump should be done with the actual curve, smoothness drop and pipes and working range.

In determining the head, the depth of the lake should not be automatically added to the height of the fountain. The energy calculation must be done with the correct reference of the free water level and the actual flow path.

47–8. Water harvesting, sediment and minimum depth

The pump inlet must have a proper distance from the bed and water level even in low water conditions. Proximity to the bed can increase sediment input, and decreasing submergence may also impair the quality of water harvesting.

The permissible working depth is a feature of the selected model. For example, Otterbine states a certain minimum depth for the Mystic set and emphasizes that the set should float. This value cannot be generalized to all floating fountains. Specifications and installation conditions of Mystic ^[312]

In this project, the following must be specified in the map:

• Alignment of the lowest component of the set;

• Its distance from the bed at the lowest water level;

• The location and open surface of the strainers;

• The method of removing the strainer for cleaning;

• Free space around the pump inlet.

Coarse filter has the role of mechanical protection. Its existence does not mean sanitary treatment of water or quality management of the entire lake.

47–9. Bracing and the forces acting on it

The containment system must keep the movement of the set within the permissible limits and also accept the change of the water level.

Effective loads include wind, current, wave, asymmetric spray forces, and cable tension. The harness capacity is not only dependent on the resistance of the rope or the tow wire; The connection to the frame, intermediate connections and shore or bed restraints must also have sufficient capacity.

In the geomembrane substrate, the placement of the weight or the implementation of the harness must be coordinated with the protection of the waterproof cover. The greater weight of a block alone does not guarantee its storage capacity; Slip, heave and bed behavior should be investigated.

Otterbine's Fractional Series Installation Guide shows examples of shore and weight harnesses and emphasizes proper cable clearance. The details of the same model are not a substitute for calculating the containment of the collection in this chapter. Otterbine Installation Guide ^[313]

47–10. The effect of water level change on containment geometry

Let's assume that the horizontal distance of the connection point on the float to the horizontal harness is eight meters. In the first case, the vertical difference is three meters.

Straight geometric distance:

$L_1=\sqrt{8^2+3^2}=8.54m$

If the water level rises two meters:

$L_2=\sqrt{8^2+5^2}=9.43m$

Change straight distance:

$\Delta L=9.43-8.54=0.89m$

This example shows that changing the water level can significantly change the containment geometry.

The number 8.54 or 9.43 meters is not the final length of the harness line. Sagging, elasticity, pretension, horizontal movement and wave conditions are not present in this simple calculation. Shortening the harness can create an undesirable vertical force, and loosening it too much can increase assembly displacement.

Figure note from the source manuscript

Figure 3-47: Cross-section of anchorage at two water levels

The fixed bedding harness, the horizontal distance of eight meters and the level difference of three and five meters should be displayed. Straight lines are simply defined as "geometric distance"; The actual path of the containment line requires a separate analysis.

47–11. Cabling and voltage drop calculation example

In the floating fountain, the long distance to the shore can determine the choice of cable and the location of power sources.

For 12 18W lamps:

$P_{lighting}=12\times 18=216W$

At a voltage of 24 V, the calculated nominal current:

$I=\frac{216}{24}=9A$

Let's assume that the entire load is fed from a copper path with a one-way length of 50 meters and a cross section of 6 square millimeters. For initial approximation, we consider the specific resistance of copper to be $0.0175\Omega m{m}^2/m$:

$R_{loop}=\frac{2{\rho }_{e}L}{S}$

$R_{loop}=\frac{2\times 0.0175\times 50}{6}\approx 0.292\Omega$

Voltage drop in the hypothetical current of 9 amps:

$\Delta V=IR=9\times 0.292\approx 2.63V$

$\Delta V\%=\frac{2.63}{24}\times 100\approx 10.9\%$

This estimate does not take into account the resistance of connections and the increase in resistance due to temperature. The actual behavior of the LED driver may also change the current. The method of calculating the voltage drop and the load conditions should be checked in the selection of the circuit. Schneider Electric voltage drop calculation guide ^[314]

Splitting the load into several circuits, increasing the cross section or revising the feeding location are options to consider. The final selection should cover the voltage range of the equipment and the electrical requirements in the vicinity of the water at the same time.

47–12. Cable protection and control of environmental conditions

The power cable should not play the role of harness line. Its path must accept the change of surface and movement of the assembly, without entering the suction area, under the wear points or in the path of the boat.

Connections, glands and cables should be selected for actual installation conditions. The IP68 title of a component does not prove the complete safety of the electrical system.

In its accessories, Otterbine introduces mechanical cable protection and wind and water level controls; These cases show that the environmental conditions are part of the system design. Otterbine peripherals and controls ^[315]

For the present example, the control logic should cover the following situations:

Numerical limits of these situations should be obtained from design and site testing.

47–13. Demonstration fountain and lake quality management

Water movement and splashing alone do not prove that the oxygen demand or water quality of the entire lake is met.

For example, in introducing the Mystic, Otterbine specifies that this model is not intended for water quality management. This difference should be observed in the definition of the purpose of purchase. Mystic declared user

If the purpose of the project is to improve water quality in addition to demonstration, its independent characteristics should be determined: the volume and depth of the zone, seasonal conditions, pollution load, dissolved oxygen and the required performance of the equipment.

Also, the water fountain maintenance program should take into account the cleanliness of the entrances, the condition of the sediment and bio-layer, and the risk of spreading droplets to the users' area. Chemicals from a ponded watershed cannot be extrapolated to a lake with aquatic life or environmental relevance without investigation.

47–14. Installation, transfer and maintenance

The method of removing the complex from the water must be known before construction. In this example, controlled transfer to a shore service facility is the basis option under consideration.

Executive documents should include lifting points, carrying mass, water drainage status of equipment and method of disconnecting connections. Connecting the crane to a part of the frame that is not designed for lifting is not acceptable.

The maintenance plan should also cover the following:

• Visiting the chambers and signs of changing the watercourse;

• Cleaning filters and controlling pump performance;

• Inspection of corrosion and metal connections;

• Inspection of wear of harnesses and cables;

• Registering the position and balance of the collection;

• Seasonal action appropriate to freezing, flooding or water depletion.

The presence of the technician on the fountain will be allowed only if this user is predicted and approved. Otherwise, repair should be done from a suitable access platform or after the set has been moved.

47–15. Test and delivery

Project deliverables should document float behavior in addition to spray shape.

The damage or stability test should not be done by introducing water into the vessels or by improvising the transfer of people. The test method, load and stopping limits must be determined in advance by the responsible designer.

Figure note from the source manuscript

Figure 47–4: Installation or repair documentation from the GSO archive

Choose a picture of the set on the beach and a picture of the floating state after installation. Anchoring points, cable route and floating compartments should be marked in the picture. The name and description of the actual project services should be included in the subtitle.

47–16. Study results and supplementary documents

To complete the design, calculations of intact and damaged stability, environmental loads, containment and bed capacity, electrical layout, suction conditions, and repair methods must be finalized.

The operation file must clearly record the mass and allowed arrangement of the equipment, the water level range, the stopping conditions and the method of transfer to the shore. Any subsequent changes in the equipment or their location must also be adapted to these principles; Because in a floating fountain, changing one component can affect the display, balance and bracing at the same time.