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Flow rate is a quantity that expresses how much substance passes through a cross-sectional area over a specified time. The amount of fluid is typically quantified using its volume or mass, depending on the application.

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The maximum flow rate tells you the upper limit of how much fluid can be transferred through an object within a specific time interval. For example, the larger it is for a tap, the faster you can fill a bath.

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To determine fluid velocity from the volumetric flow rate, you need to divide it by the cross-sectional area of the substance.

To find the mass flow rate, you need to multiply the volumetric flow rate by the density of the substance. This relation is easier to remember if you recall that density is the quotient of mass and volume.

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Don't forget that our tools are flexible, so you can use this calculator as a pipe velocity calculator. You can, for example, determine the water velocity of your faucet, given the diameter (e.g., 0.5 in0.5\ \mathrm{in}0.5 in) and flow rate of a kitchen faucet (the usual range is 111 gallon - 2.22.22.2 gallons per minute, depending on the aerator type). By the way, have you seen our tap water calculator, which shows your savings if you were to switch from bottled to tap water?

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As l/tl / tl/t is the volume length divided by time, you can see that it's just the flow velocity. So, the volumetric flow rate formula boils down to:

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where A is a cross-sectional area of the fluid, and lll is the width of a given portion of the fluid. If our pipe is circular, it's just the formula for to calculate the cylinder volume. Substituting the above formula to the equation from the flow rate definition, we obtain:

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Input the measurements needed to compute cross-sectional area. If the cross-section is a circle or square/rectangle, you'll find that option on the list. In every other case, you can type the area value directly into the calculator (you can use our comprehensive area calculator to help you). Let's choose a pipe with an internal diameter of 3 in3\ \mathrm{in}3 in.

And there it is, the first part of the calculations is done: the tool has worked as a volumetric flow rate calculator. We've found out that the volumetric flow rate is 0.4909 ft3/s0.4909\ \mathrm{ft^3/s}0.4909 ft3/s. Remember, you can always change the units, so don't worry if you need to work in gallons/minute or liters/hour.

Believe it or not, our flow rate calculator is not only useful in fluid mechanics but also in everyday problems. It will not only help you if you want to find the flow rate of a garden hose or shower head but also if you're curious about how much blood your heart pumps every minute (what we met at the cardiac output calculator). It may also serve as a simple pipe velocity calculator.

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Another related concept is mass flow rate, sometimes called mass flux or mass current. This time it's not the volume, but mass of a substance that passes through a given cross-sectional area per unit of time. It is an essential measure when purifying water in a wastewater plant.

When we talk about flow rate, you most likely picture the concept of volumetric flow rate (also known as rate of liquid flow, volume flow rate or volume velocity). The volumetric flow rate can be defined as the volume of a given fluid that passes through a given cross-sectional area per unit of time. It's usually represented by the symbol QQQ (sometimes V˙\dot{V}V˙ — VVV with a dot)

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If you know the density, you can calculate the mass flow rate as well; just input the density of the flow material. In our example, water has a density of approximately 998 kg/m3998\ \mathrm{kg/m^3}998 kg/m3 (the density of water at 68 °F68\ \mathrm{\degree F}68 °F, or 20 °C20\ \mathrm{\degree C}20 °C). However, if you want to be super accurate, check out our water density calculator, as the density changes with temperature, salinity, and pressure.

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First, select a shape from the list. For this example, we'd like to know the flow rate of water in a circular pipe, so we will select the circular (pipe) option.

The volumetric flow rate formula may be written in the alternative (read: way more useful) form. You can first calculate the volume of a portion of the fluid in a channel as:

For a complete understanding of the topic, you can find a section explaining what the flow rate is below, as well as a paragraph helping to understand how to calculate the flow rate. Be careful, as the term "flow rate" itself may be ambiguous! Luckily for you, we've implemented two flow rate formulas, so you're covered in both cases. This means that our tool may serve as both a volumetric flow rate calculator (i.e., we can use it to calculate the gallons per minute) and a mass flow rate calculator.