In my previous article, published at https://www.aqa.ru/doc.php?docid=97, I outlined the work in the most general terms. **aquarium filters**. I had to cut something and add something to make it clearer. The result was an article focused on an unprepared reader.

However, the operation of filters, especially those equipped with a pump, as I think, requires more detailed study, because many people do not understand why their filter works this way and not otherwise. Therefore, there is a need for such articles. They are, but they have a specialized and non-event character. Those who want to get acquainted with such literature can refer to those links in more detail, which I will give at the end of my article.

I did not begin to rewrite the old article, so some topics will be repeated, but with a more detailed study of the processes. And it will not be specialized, but aquarium, but using specialized terminology.

On the forum *Filtration* Frequently asked questions related to improper operation of pump aquariums *of filters*. Someone asks why the new filter works less than what is indicated in its characteristics. Someone complains about reducing the length of the jet coming out of *filter*, after a period of operation. Someone says his *filter* flows in the off state or with a fully open inlet tap and covered outlet when running. Someone asks why his inner *filter* does not suck in air, but squeezes out water through a connected air hose.

All questions can be answered if you know how the pump filter works. What processes occur with water in the aquarium filtration system. What factors affect the performance of aquarium filters.

This article will not answer the above questions. Answers to them can be found on our forum: www.aqa.ru/forum in the section Filtering and Other Equipment. The article is intended only for familiarization with the operation of pumps and losses in filtration systems caused by hydrodynamic processes occurring in them.

I’m not going to paint the equations of hydrodynamics, deduce formulas and equations. I’ll just point out some basic dependencies related to aquarism that you don’t need to know by heart, but it’s advisable to have some kind of concept about them. But I will paint the basic equations from different sides.

The following text is a simple rewriting of the basic equations of the course of Hydrodynamics, with my adjustment of formulas, for their correct display on computers with different encoding of the text. The letters of the Greek alphabet were replaced by me in Latin and Russian, while preserving the basic meaning and connection of different formulas with each other.

Pump (from the English. Pump – pump) of any aquarium filter creates a flow of water, sucking water and driving it through the filter materials. The volume of water per unit of time passing through any cross section of the filtration system will be exactly the same. This is true for any pump. The pump cannot suck water more or less than it drops. How much water has come, so much has happened.

Unlike the ideal fluid, which is considered incompressible and not having friction, real liquids have such friction. In addition, they have a viscosity, or internal friction. This also applies to the water filling the aquarium.

In solids, in the case of an attempt to change their shape (for example, when one part of the body is displaced relative to another), an elastic shear deformation force appears that is proportional to the displacement of atoms located in the lattice sites of neighboring atomic layers. In a liquid, this force is proportional to the magnitude of the change in velocity observed when passing between adjacent layers of interacting molecules.

The movement of a real fluid is easy to understand if you imagine a cross-section of a tree trunk, on which annual rings are visible. The bark of the tree will correspond to the walls of the pipe, and the rings to the location of the layers of fluid flowing at different uniform speeds. The outer annual ring will correspond to the layer where water adheres to the pipe walls. In this layer the water does not move. Its speed is zero. Each fluid layer, located closer to the middle of the pipe, will carry the adjacent layer, which is located closer to the pipe surface. The force with which one layer of fluid pulls the other, the next layer, will be equal to the force with which that layer retards. Forces will be equal, but directed in opposite directions. The highest speed will be at the layer flowing in the middle of the pipe, which corresponds to the central annual ring of the saw cut of the tree in my example.

It should be emphasized that the flow of water must be considered from this point of view not only in pipes and hoses. In any place of the hydrodynamic system, on any surface in contact with the moving water, the flow velocity in the water layer on this surface will be zero. Therefore, in this layer there are deposits of salts or colonies of bacteria settle.

Head losses directly depend on the flow rate. The higher the speed, the greater the loss. When the flow rate decreases, the losses will also decrease. You can say the opposite. The greater the pressure loss in the filtration system, the lower the water velocity will be. Why is that? Because, in addition to hydrodynamic pressure losses, there are pressure losses that increase with time – colonies of bacteria and accumulation of debris in the filter.

A centrifugal pump with a wet rotor, because water flows between the stator and the rotor, which is the aquarium pump, obeys the same laws of hydrodynamics as all the others.

During operation, the pump creates a pressure difference before and after itself.

Here you need to make a comment.

In Hydrodynamics, it is customary to count the pressure, taking atmospheric pressure as the zero point (Ratm. = 0). If the pressure in the system is greater than atmospheric, then it is called gauge and recorded with a plus sign. If the pressure is less than atmospheric, then it is called a vacuum pressure, or vacuum, and recorded with a minus sign. Therefore, they talk about positive and negative pressures. Pressure is measured in meters of water column, in Pascals, bars, atmospheres, kilograms of force per square centimeter.

Before the pump pressure will be less than atmospheric, that is – negative, or rarefaction. After the pump – more atmospheric, positive, or just pressure. The sum of the vacuum values (modulo) and pressure is equal to the pressure of the pump or pump.

Both pressure and vacuum in a working pump manifest themselves when some kind of load is attached to it. For example, a filter, hoses with a suction pipe and a flute, a flow reactor of carbon dioxide and so on. If the pump is simply fixed in the aquarium to create the movement of water, then vacuum and pressure will be created only inside the pump casing, in its water supply channels, as they will create some resistance to the movement of water. Outside there will be only the flow of water. To the pump, and from her. I will tell more about currents below.

One of the main laws of hydrodynamics is the law of conservation of energy. This law, as applied to hydrodynamics, is described by the Bernoulli equation and sounds like this:

Total energy flow of an ideal fluid __steady state laminar flow__ equal to the sum of the kinetic and potential energies. The less the potential energy of water becomes, the more kinetic will be. Conversely, with increasing potential energy, the kinetic will decrease. But the total energy will remain constant.

The total energy of the fluid flow, or the total pressure, as it is called in Hydrodynamics, is determined by the maximum difference in the levels of the pumped liquid in two tanks opened from above, filled with this liquid, and expressed in linear units (meters of water or millimeters of mercury or alcohol) ).

A variant of writing the Bernoulli equation, expressed in units of pressure, in applying it to __steady fluid flow__, looks like that:

(pV ^ 2) / 2 pgH P = N = const,

where p is the density of the fluid

V is the flow rate

H is the height at which the fluid element is located,

N – full pressure,

(pV ^ 2) / 2- the kinetic energy of the fluid, or the dynamic pressure,

(pgH P) – potential energy of the fluid, or static pressure,

where pgH is the weight pressure of the liquid column,

P – pressure exerted on the liquid.

As can be seen from the equation, the kinetic energy of a liquid, or dynamic pressure, is determined by the velocity of the liquid, and the potential energy of the liquid, or static pressure, is determined by the height to which, with a given total energy expended, this liquid can rise relative to the level of the liquid in the supply tank.

is the main law of hydrostatics – the law of Pascal.

It should be noted that the Bernoulli equation describes the energy __fluid element__ in various hydrodynamic systems. But what simply looks like formulas will be quite difficult for a wide audience to understand, so I’ll skip the conclusions of the equations, leaving the equations themselves in a readable form.

The flow of water passing through the filtration system encounters various obstacles in its path. He is experiencing the effect of gravity, the force of friction of water on the walls of hoses, on the walls of the body, on the fillers of the filter, local resistance to pressure, in the form of internal construction channels, bends of hoses and rigid connectors, water intake pipe and output flute. All these obstacles determine the speed __steady state__ water flow in any real hydrodynamic system.

For __real__ liquid, which is aquarium water, the Bernoulli equation should be written in the form:

(pV ^ 2) / 2 pgH P Nn = N = const,

where Nп – the total loss of pressure of the fluid flow. Head losses are expressed in linear units, as well as head.

This equation will be true for any filter and pump, even slightly raising the water above the surface of the water in the water intake tank, because it can be not only an aquarium.

For any filter that does not raise the water above the surface of the water in the aquarium, the equation of total pressure will take the form:

(pV ^ 2) / 2 Nn = N = const,

since P = 0 and H = 0.

For two points corresponding to the sections of the pipeline section, along which the fluid, marked 1 and 2, is transported, as the fluid moves, the Bernoulli equation can be written as:

Where N1 and N2 – the pressure of the fluid flow at the beginning and end of the segment, respectively.

The total loss of pressure of the fluid flow Nп consists of the pressure loss of __length__ flow rate and head loss __local__ resistance Nm:

Therefore, when evaluating losses in any filtering system, in no case should you reject any recurring sections from consideration. These areas will have their own resistance to pressure, and these resistances should be added up and not subtracted from each other.

Loss of pressure on the friction along the length of the flow, arising from a uniform pressure flow of fluid in the pipes, is determined by the equation:

where L is the dimensionless coefficient of hydraulic friction, equal to

L is the length of the pipe section,

Vav – the average flow rate

d is the internal diameter of the pipeline,

g – gravitational acceleration,

Vd – dynamic flow rate.

Therefore, it is impossible, in the calculations, to discard the canister hoses. Friction losses in them will depend on their length and diameter. The shorter the hoses, and their diameter is larger, the less friction losses will be in them.

The hydraulic friction coefficient for steady-state laminar flow can be obtained from the Darcy-Weisbach equation:

L = 64Vsr / dVsr = 64 / Re,

where Re is the Reynolds number, determined by the formula:

where p is the density of the fluid

Vav – average (pipe section) flow rate,

R is the radius of the cross section of the cylindrical pipe,

m – coefficient of viscosity.

The same coefficient of hydraulic friction for a turbulent flow is determined as a function of the Reynolds number:

With an increase in the Reynolds number, the dependence graph deviates from a straight line and goes into a second-order curve.

Reynolds numbers for different pipe diameters and flow rates are tabulated.

Local head loss, Nm, is determined by the formula:

where T is the local resistance, or equivalent length, for a given pipe diameter (Lekv).

In addition, for filters, the Borda formula should be used, which characterizes the dependence of the pressure loss during a sudden expansion / contraction, when water enters / exits to / from the filter / a:

Or: T = (1 – S1 / S2) ^ 2,

where S is the cross-sectional area (for example, hose / canister).

Applying the law of conservation of energy, determined by the sum of kinetic and potential energies: Е = Ек Еп, and considering that the location of the input and output hoses of the external canister filter, in most cases, coincide in level, that is, H = 0, the Bernoulli equation can be written as:

(pV ^ 2) / 2 Nn = N = const.

Expressing from here the speed, we obtain the dependence of the flow rate of the liquid on the magnitude of the total pressure, the total pressure loss and density of this liquid:

That is, the variant of writing the Torricelli formula for the flow __real__ fluid. This equation will also be true for internal filters if they do not lift the water above the surface of the water in the aquarium.

For filters that raise water to a certain height, the equation of speed will be:

V = (2 (N – pgH – P – Np) / p) ^ 1/2.

Head losses occurring as the filter and canister hoses become dirty can be clearly seen from the shortening of the jet flowing out of the output hose.

The water passing through the system acquires kinetic energy imparted to it by the pump. Flowing out of the system, it moves by inertia. With the horizontal arrangement of the outlet pipe, the jet in the air first moves straight, gradually deviating downward under the action of gravity. If the water level in the aquarium is kept constant, then after a while, there will be a noticeable shortening of the jet length caused by biological fouling of the internal surfaces of the filtration system and filter media.

In Hydrodynamics, the force of the jet of fluid exiting the pipe is also called pressure. This is the dynamic pressure of the fluid flow, equal to the difference between the total pressure of the flow and its static pressure, taking into account the loss of pressure in the system. This pressure creates a current in the aquarium, of which I spoke above.

If pressure __in a jet__ flowing out of the hose, equal to atmospheric pressure, P = Ratm = 0, then the pressure itself __jet__, or dynamic head, will be equal to

(pV ^ 2) / 2 = N – (pgH P Nп).

From this equation we can see the dependence of the flow rate of water on the height of the drain installation with respect to the total head of the pump. With increasing height H, the flow rate will decrease, and, with decreasing height, increase. Considering that the pumped liquid is aquarium water, in our case, with N = H, that is, when the total pressure of the pump coincides with its static pressure, the flow rate and pressure loss will be zero, V = 0 and Nп = 0.

Another main characteristic of the pump is consumption. The flow rate is the amount of fluid pumped per unit of time, for a given difference in level between the supply and receiving tanks. This difference in levels should not be greater than the pump head. Otherwise, water will not flow at all. The pump will only raise the water to a height equal to the pressure, and will maintain the water at that height.

The flow rate of the fluid in the cross section of the flow is calculated by the equation of continuity of flow (mass conservation) for an incompressible fluid:

Vav – the average rate of fluid flow,

S is the area of the living cross-section of the pipe.

Knowing the height of the maximum head, the density of water, measuring the water flow in the current filtration system, with a head equal to zero, by calculating the flow rate, we can determine the total head loss for this water flow rate:

The actual pressure loss in the filter can be, for clean filter materials that occupy the same volume, from 10 to 70 percent, depending on what the filter material is made of!

Let me draw attention once again to the fact that most of the above equations are operating on the flow rate of water and its connection with height and pressure in the filtration system.

Manufacturers of pumps or pump filters indicate head and flow rates. The head usually corresponds to the full head of the pump or the height of the water column, upon reaching which, when the pump is running, the water flow rate is zero. And the flow rate usually corresponds to the amount of water pumped by the pump, in the absence of a difference in height between the inlet and outlet water. Manufacturers usually do not indicate the flow of water through filtering materials, but this flow significantly affects the performance of the entire filtration system.

We must not forget about the bacteria and algae that settle in the filtration system, creating additional resistance. About trash that enters the filter from the aquarium.

Biological changes also contribute to the loss of pressure and water flow through the filter. If the physical losses can be calculated by applying the formulas of Hydrodynamics, then the biological losses can be calculated poorly. We can only assume how the filter will work under certain biological loads.

In aquariums with a large biological load, for example, in aquariums with cichlids, goldfish or turtles that are not friendly with live plants, the drop in filter performance occurs very quickly. In aquariums with fish and plants, this is much slower, because some of the fish secretions are consumed by plants.

Because of the different, individual taste preferences of different owners of different aquariums, it is extremely difficult for him to advise on the choice of filter or pump. All tips are empirical, drawing on the different experiences of different people.

The most common advice is to choose the performance of the pump according to the volume of the aquarium. Usually they take a pump whose performance, according to various recommendations, is 2-4, or 3-5 volumes of aquarium water per hour. Just need to remember about biological fouling!

If new, clean fillers give a filter performance, not a pump, 2-4 volumes per hour, then a colony of bacteria that will live on them can reduce this productivity several times. Therefore, you need to buy a filter with a pump, or a pump for it, with a margin for losses.

For example, for an aquarium with an average population of fish and a certain number of living plants with a volume of 100 liters, according to the recommendation given, you need a filter with a capacity of 200-400 (300-500) liters per hour. What does it mean? This means that a filter that has been populated with bacteria for a long time should have a capacity of 2-4 (3-5) volumes of the aquarium per hour, and not the performance of the pump of a filter that has absolutely clean filter media.

How to count? And read this:

- Aquarium 100 liters. We need a filter with a pump on 200-400 (300-500) liters per hour.
- Add 10-15 percent of the head loss in a clean filter material. It turns out 220-460 (330-575) liters per hour.
- Add to the numbers obtained the loss of biological fouling of the entire filtration system. Another 10-50 percent. Get about 250-870 liters per hour. This is the performance of the pump, not the filter! A filter with bacteria on such a pump will produce 200-500 liters per hour. Why did I bring 10-50 percent? So after all the filter also needs to be washed sometimes. And canister filters also clean the hoses from the inside. The numbers, as I said above, are empirical, medium-ceiling, oriented to the average aquarist with a medium-ceiling aquarium with an average population. In aquariums with live plants, the numbers will be lower than in aquariums without live plants. What will these numbers be, no one will say.
- Choose a filter model that fits these calculations. According to the recommendations, it is better to buy a filter with higher pump performance. As they say, filtering does not happen much. The excess pressure can be adjusted with taps or nozzles, and in the future, only buying a new filter can be used to increase filtration performance, or to install an additional one equipped with its own pump.

For those who do not remember, the surface area of the sphere:

R is the radius of the sphere.

The surface area of the cube:

where a is the length of the cube edge.

The surface area of the cylinder:

R is the cylinder radius,

H is the height of the cylinder.

The surface area of branded biological fillers is much larger than the surface areas of the above geometric bodies. Usually, manufacturers point it out.

Of course, 2-4 liters per hour per 1 gram of fish weight is the minimum performance for an aquarium with live plants. For tsikhlidnikov it also needs to be increased several times. And the substrate for bacteria will also become clogged over time. Its area also needs to be increased in advance.

But there is a catch. The fact is that beginning aquarists, very often, are so filled with their new aquarium with fish that there can be no talk of any average statistical value. And when young fish grow up and become larger, then the volume of waste for which the filter was calculated may simply not be enough. Therefore, the number of fish should be limited immediately before buying it, based on the opinion that determines, for example, 1 cm of the body length of an adult fish per 1 liter of water, or immediately buy a more efficient filter. When buying young fish, it is imperative to find out to what maximum sizes they can grow in the aquarium, and, based on this, select the fish population for their size.

We clean everything in our room, vacuum it, wipe off dust, scrub, and so on. We also ventilate it regularly, so that there is fresh air, and there were no odors, often unpleasant. The fish in the aquarium – a hostel, or a communal apartment, as you wish, combined with a bathroom. And besides us, there is no one to worry about them. Clean up after themselves they will not. Take care of your pets, and they will delight you with their appearance and cheerful behavior for a long time.

Konstantin Abramov (Daxel).

The following materials were used in the article: