## Hydraulics for the Reef Keeper

Many aquarists get by without knowing the first thing about the physics of water. That said, I know many of you would like to know a little bit more about the physics of water and how they govern different aspects of your aquarium. We will touch on some basic design principles such as Hartford Loops and baffles as well as some real world flow calculations using Bernoulli’s law and the basics of centrifugal pumps.

You may be thingking… “Physics? Who needs physics, this is an aquarium hobby bub?” Have you ever looked for a bulkhead flow rate calculator? Have you ever tried to figure out how much water your aquarium overflow can handle?

The driving force for writing this article is the high number of well intentioned, but poorly informed posts regarding different aspects of aquarium plumbing and flow rates. Terrible plumbing advice can be found in-bulk at just about any online aquarium forum. You will fine dozens of bulkhead flow calculators, but few of them are derived from anything more than anecodtal gueses or improperly applied physics.

### How much water flows?

One of the most common questions is “How much water will flow through a bulkhead?” We can use a fairly simple equation to answer that question. The equation is the “Bernoulli Equation”. According to Bernoulli’s Law, the uncompressible fluid (water) will travel through an opening at a velocity(v) = sqrt (2*g*h) just like any other object FALLING out of a hole. Let’s take a closer look at what Bernoulli said.

Daniel Bernoulli’s Principle:

Where:

v = Velocity

h = Height

g = Gravity

Flow Rate:

Where:

Q = Flow Rate

A = Cross Sectional Area

v = Velocity

So, we first solve for the Velocity of the water. The water has Velocity because gravity is pulling on it (it is falling).

We use the equation to find that Velocity. Once we find the Velocity of the water, we can find out how much water is falling because we know the Area of the pipe that that the water is draining (falling) through. That is, we use the equation Q = A*v to determine the flow through the hole.

I have built a simple tank discharge calculator to do the math for you. Note: This calculator only works for systems where the drain is not able to suck air in along with the water (a mode called, 2-Phase flow). That happens when air is mixed with water and it creates an entirely different set of problems that we will discuss in later installment.

The takeaway? The calculator will work as a bulkhead flow calculator as long as the bulkhead is fully submerged and does not suck in air. This calculator can also be found on the Tools page.

### Example Usage

Given a standard 1″ bulkhead that has an internal diameter of 1.033″ attached to a pipe of the same diameter, and the pipe drops 24″ to the sump. The head height would be 24″ and the Pipe/Orifice Diameter would be 1.033″. Clicking the “calculate” button will show that the maximum flow rate (full siphon) would be about 1,700 GPH.

How do you setup an overflow that works on the principle of a siphon? See the Silent and Fail-Safe Aquarium Overflow project for more information.

Check back for additions to this article. We will talk about a few other flow equations that can help us understand the flow of water in a pipe. We will also talk about the math of pumps. skimmers, baffles and other parts of the aquarium.

-Bean