Last time we saw how pulley diameter governs speed in engineering scenarios which make use of a belt and pulley system. Today we’ll see how this phenomenon is defined mathematically through which enables precise pulley diameters to be calculated to achieve specific rotational speeds. Today we’ll apply this Pulley Speed Ratio Formula, to a scenario involving a building’s ventilating system.Formula The N × _{1} = D_{2}N (1)_{2}where, D the diameter of the driven pulley._{2}
The pulleys’ rotational speeds are represented by N, and are measured in revolutions per minute (_{2}RPM). Now, let’s apply Equation (1) to an example in which a blower must deliver a specific air flow to a building’s ventilating system. This is accomplished by manipulating the ratios between the driven pulley’s diameter, D. If you’ll recall from our discussion last time, when both the driving and driven pulleys have the same diameter, the entire assembly moves at the same speed, and this would be bad for our scenario._{1}An electric motor and blower impeller moving at the same speed is problematic because electric motors are designed to spin at much faster speeds than typical blower impellers in order to produce desired air flow. If their pulleys’ diameters were the same size, it would result in an improperly working ventilating system in which air passes through the furnace heat exchanger and air conditioner cooling coils far too quickly to do an efficient job of heating or cooling. To bear this out, let’s suppose we have an electric motor turning at a fixed speed of 3600 In this example known variables are inches, N = 3600 _{1}RPM, and N = 1500 _{2}RPM. The diameter D is unknown. Inserting the known values into equation (1), we can solve for _{2}D,_{2} (3 RPM) (2)Simplified, this becomes, = 7.2 inches (3)Next time we’ll see how friction affects our scenario.
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