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We’ve been working our way towards developing values for variables in our example pulley-belt assembly, and last time we calculated the velocity of the belt in that assembly to be 237.99 feet per minute. But before we can go on to calculate the belt’s loose side tension, T2, and tight side tension, T1, we’ll need to discuss unit conversion, specifically how to convert horsepower into foot-pounds per second. Our working formula for this demonstration is the formula for mechanical power, P, previously introduced and shown again here, P = (T1 – T2) × V (1) By engineering convention mechanical power is normally measured in units of foot-pounds per second. But if you’ll recall from a past blog in which we determined the belt’s velocity, V, it was measured in units of feet per minute, not per second. To further complicate things, the difference in belt tensions, T1 – T2, is stated in units of pounds, and combining these elements together results in P being expressed in foot-pounds per minute, not the required per second, because we are multiplying feet per minute by pounds. That’s a whole lot of unit changing within a single equation, which makes for an awkward situation. To smooth things out we’ll have to do some converting of units. We’ll start by dividing V by 60 seconds per minute so it can be expressed in units of feet per second, V = 237.99 feet per minute ÷ 60 seconds per minute (2) V = 3.93 feet/second (3) The power in our belt was previously given as 4 horsepower, which must also undergo conversion and be put in terms of foot-pounds per second so it can be used in equation (1).
Unit Conversion, Horsepower to Foot-Pounds per Second
One horsepower is equal to 550 foot-pounds per second, which makes the amount of power, P, in our pulley-belt assembly equal to 2,200 foot-pounds per second. Units converted, we can now insert the values for V and P into equation (1) to arrive at, 2,200 foot pounds per second = (T1 – T2) × 3.93 feet/second (4) Next time we’ll use this relationship to develop values for T1 and T2, the belt’s tight and loose side tensions. Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |
