Pressure as a function of time.

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Homework Help Overview

The discussion revolves around determining pressure as a function of time in a fluid dynamics context, specifically involving water levels in a tank with varying inflow and outflow rates. The original poster seeks to understand how to express pressure in relation to time, given initial conditions and cross-sectional areas.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to find the height of water as a function of time to subsequently calculate pressure. Questions arise regarding the net flow rates of water and the implications for pressure at different points in the system.

Discussion Status

There is an ongoing exploration of how to relate the changing water level to pressure calculations. Some participants are questioning the specifics of pressure measurement and the effects of varying flow rates, while others are attempting to clarify the relationship between height and pressure.

Contextual Notes

Participants note the absence of an attachment that may contain additional information. There is also uncertainty regarding the definition of pressure being sought and the complexity introduced by non-homogeneous flow conditions.

wwshr87
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Homework Statement



Find pressure as a function of time. At time t = 0, the water level is 2 feet.
Cross-sectional area is 8 ft2 for the top and 1 ft2 for the bottom.
Please see the attachment for further information.

Homework Equations



p=(ro)gh

The Attempt at a Solution



Since I want to find the pressure as a function of time; I will need to find h as a function of time, then multiply by ro and g. How can I do this?

Thanks
 
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There is no attachment. I assume water is flowing out somewhere?
 
Water in flowing in at a rate of 3-t, and flowing out at a rate of t^2. Initial water level is 2 ft.

I'm sorry I am new to this. I tried attaching the file again. Thanks.
 

Attachments

  • waterpressure.JPG
    waterpressure.JPG
    12.4 KB · Views: 507
Which pressure do you want to find? Pressure on the pipe, pressure of the water flow at the lower pipe, etc?
 
I want to find the pressure at the bottom of the tank.
Thanks
 
I'm not sure what you meant by "pressure at the bottom of the tank". Forget it for a while. Back to your main problem, finding h. From the two water flowing rates, you can calculate the net rate at which water gets in/out of the top pipe, can't you? And from the relation: [tex]\frac{dM_{net}}{dt}=\rho S_{top}\frac{dh}{dt}[/tex], it's easy to find dh/dt and h. What is the dimension of [tex]\dot {M}[/tex] by the way?

The main problem I want to talk about is the pressure. From your equation [tex]p=\rho gh[/tex], I can guess that you want to find the pressure exerting on the bottom, correct? It is not easy at all. If you look at it more carefully, the pressure on the bottom near the edge is different from the pressure at the places farther. The flow's speed is not homogeneous in the lower pipe. Moreover the pressure due to the water flowing in must be taken into account.
 
Last edited:
I have attached the solution I have for this problem. The part I do not understand is how they calculate dv/dh.
 

Attachments

  • pressuresolution.JPG
    pressuresolution.JPG
    18.4 KB · Views: 603
Sorry, I don't get it either.
 

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