Mass flow rate, or mdot, is a very important concept to understand and a very good tool to possess. Mdot is the lead variable in determining orifice size pertaining to injection of fluids, throat of nozzles, and is very analogous to the draining of a battery.
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Mass flow rate is the rate the mass of a fluid passes through a cross sectional area. Consider a garden hose with water flowing from the end. To help understand the mathematics behind it there are some basic concepts to understand.
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The first basic concept is that matter cannot be created or destroyed. In addition, density is equal to the mass of a fluid divided by its volume.
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Playing with the density formula shows a relationship between mass and volume. Therefore, one can derive a mass by knowing volume of the fluid. Consider again, the garden hose. Knowing that water weighs about eight pounds per gallon, derived from density of water, then one could easily establish the mass flow rate if they knew the volume of the water flow out the end of the hose.
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When considering flow rate through a tube, or cross sectional area, a formula can be found with a simple relationship of a few variables. Consider when the fluid is passing through the tube – what variables would influence the mass of the moving fluid? The area of the tube, the velocity of the fluid, and the time of flow.
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Velocity can be understood as length divided by time (same as distance/time such as mph) and can replace the velocity variable.
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Velocity can be understood as length divided by time (same as distance/time such as mph) and can replace the velocity variable.
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The time variables will simplify to Area times Length.
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The time variables will simplify to Area times Length.
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And we earlier stated that mass flow rate was a volumetric issue. With the simplified variables we see that Area times Length is equal to volume.
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Considering a fluid passing through a cross sectional area at a certain velocity a volume of mass passing through can be defined based on an amount of time.
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We can also replace volume with mass divided by density.
By multiplying density across both sides we can simplify the left side of the equation.
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And since we are dealing with mass flow rate, the time on the right side of the equation should be brought over, creating mdot being equal to density of the fluid times the cross sectional area times the velocity of the fluid. Put in your notes and be ready to use it in the future. It is one of your many tools. 15