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# Fluid Flow Exponential Decay.

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Introduction

Fluid Flow Exponential Decay. Experiment 4 was the study of exponential decay and how closely a fluid flow follwed the half-life trend. The experiment was carried out by filling a tall cylinder with water to a known height. The water is then allowed to flow out of a small capillary tube at the bottom. The first part of the experiment tested how the height of the water column affected the pressure exerted by air on the water, which in turn affected the rate of the water flow, the height of the water was kept constant for each event. By comparing the amount of time needed to collect roughly 100ml of water at varying heights of water, it was found that the higher the column of water the faster the rate of water flows. ...read more.

Middle

To find the value of Q, we used the equation Q = ?(diameter/2)2?h. Experimentally, the data collected fit together very well graphically. In both graphs of [?Q/?T vs P] and [?Q/?T vs Q], the data collected fit the linear fit line very well. Because the data fit very well onto the linear best fit line, we can see that the rate of change of Q over time is directly proportional to both Q, the initial amount of water, and P, the pressure exerted on the water. This proportional relationship between [?Q/?T vs Q] was found to be 0.00235 and the proportional relationship between [?Q/?T vs P] was found to be 0.12219. ...read more.

Conclusion

The value of Q used in the equation was 382.8g and t was 100.3 s. This point was chosen because of it's position on the quadratic fit line of the Q vs Time graph. Using this found decay constant, we are able to calculate the theoretical half-life T = 241.5s using the computed equation kT = -0.693. According to the data collected the experimental half-life is 237.06s, the amount of time that passed before Q was half that of the Qo. The % difference of these two values came out to 1.82%. This percent error could be attributed to the coordination between the reading of the time and the reading of the height of the water. From the collected data, it is found that for the fluid flow experiment, the formula relating Q and Time was found to be Q = Qoe^-0.693t. ...read more.

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