Predicting Water Height as a Function of Drain Time: Hydrodynamics Lab Inquiry

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Homework Help Overview

The discussion revolves around predicting the height of water as a function of time for water draining from an orifice, as part of a hydrodynamics lab inquiry. Participants are attempting to determine the relationship between water height and drain time both experimentally and theoretically.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses confusion about the task requirements and the necessary steps to predict height as a function of time. Another participant seeks clarification on the appropriate formula for this prediction. A third participant describes their approach using flow rate equations and provides specific data points, while questioning their calculations and results. Additionally, one participant suggests that a differential equation may be relevant to the problem.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts and calculations. Some guidance has been offered regarding the potential involvement of differential equations, and there is an exploration of different interpretations of the problem. However, there is no explicit consensus on the correct approach or solution at this stage.

Contextual Notes

Participants are working with specific data points, including the volume of water collected and the area of the orifice, but there are indications of uncertainty regarding the formulas and methods to apply. The original poster mentions having all necessary data but lacks clarity on how to proceed.

formulajoe
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im supposed to predict height as a function of time for water leaving an orifice. determine heaigh as a function of drain time experimentally and compare the two on the same graph.

i don't even understand what it wants. I am pretty sure I've got all the necessary data, but i don't know how to do what he wants.
 
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okay, i think i have some of it figured out. but i don't know what formula to use to predict predict height as a function of time for water leaving the orifice.
 
heres what I am doing. please correct it because this is driving me insane.

im using V/t= AV. this is just different forms of the flow rate. i know the amount of (volume) of water i am gathering. it is 100 ml. i want to know how long it takes to get this amount. my lab partner found the area of the orifice to be about .15 cm^3. and I am using (2*g*h)^1/2 as the velocity. using this i end up with a time of about 357 seconds for 18 cm of height. so i checked the area of orifice using my collected data. for 100 ml of water to be collected, it too approx 4.06 sec. this is at 18 cm of height. using this, the area was around 46.
what am i doing wrong?
 
formulajoe,
what level of physics is this?

There could be a (simple) differential equation involved here. The flow rate at the oriface will be determined by the pressure at the level of the oriface below the water's surface. This will of course change with time. if the amount of water that you are extracting doesn't change the water level significantly (i.e. if the reservior is very wide), then this is probably not the case.
 

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