Lab 7 - Lab 7 Using Numeric Integration to Estimate Liquid...

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Lab 7: Using Numeric Integration to Estimate Liquid Level in a Tank From Flow Rate Measurements Often when conducting an experiment or designing a system, a rate of change is easier to measure than a total amount. For example, it is relatively easy to measure the rate of flow of a liquid but more difficult to measure the specific volume of liquid that is moving past a given point. So instead of measuring the amount of liquid, the flow rate is measured and numeric integration is used to estimate the total volume of liquid. In this lab, we will be making use of this idea in order to determine the amount of water stored in a water tower and whether we need to pump additional water into the tower. Part A of the lab gives you some practice in using numeric integration to determine the water level in a tank based on flow rates in and out. In part B, you will assume constant flow rates to simulate the process of water leaving a tank due to use and pumping water into the tank once the level in the tank falls below a given level. Finally, in part C, you will use the data file provided to simulate the water tower system using a non-constant water usage (flow rate out). A. Flow Rates and Numeric Integration Practice For all of the activities in this assignment, we will assume that the tank is cylindrical in shape with a radius of 5 meters and a total height of 20 meters. Therefore, we can determine the total volume of the tank using the equation for the volume of a cylinder: V = π r 2 h We can also use this equation to determine the volume of liquid in the tank for any arbitrary water level by simply plugging in the current water level for the height. This equation results in a volume in m 3 . However, the volume of water (at least in the US) is normally measured in gallons. Volume in m 3 can be converted to a volume in gallons using the conversion below: V gal = V m 3 0.0038 That last piece of information we need is how to get to a volume from a rate of flow. First off, if we have water
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