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Deriving a mathematical model for a fluid system.Help.

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1

$begingroup$

ive been trying to derive a mathematical model for the system shown in the image

The case is a pump, pumps water into a Column. The drain of the column is blocked. Thus there is only flow in.

i know i should end up with a differential equation of some order. Which i must solve resulting in an equation for Qin (flow in). The problem is i cannot grasp how to derive the differential equation from the capacitance and resistance of the system.

i know that resistance(fluid) = Change in level difference divided by change in flow rate

and capacitance (fluid) = change in volume of liquid stored/ change in head

Interance is ignored.

Laminar Flow is assumed for now to remove the need to decide between laminar or turbulent flow.

I know that these 2 are the analogy of electrical resistance and capacitance.

An experimental pump voltage and was applied in the lab and a flow rate recorded. Column volume and cross sectional area are know. all the values of the information is supplied in the attached image.

Realy im looking for guidance on deriving differential equations form systems.
Pleas help been starring at this for 10+hours. Dieing internally.

]

mathematical-modeling fluid-dynamics

share|cite|improve this question

edited Mar 22 at 0:54

Alex Chala

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. I don't see how your question has anything to do with modular arithmetic, so why did you use the "modular-arithmetic" tag (About modular-arithmetic gives a description of this tag)?
  $endgroup$
  – John Omielan
  Mar 22 at 0:34
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Apologizes. Thats meant to be mathematical-modeling. Ill try edit it
  $endgroup$
  – Alex Chala
  Mar 22 at 0:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  No worries. Mathematical-modeling makes a lot more sense.
  $endgroup$
  – John Omielan
  Mar 22 at 0:54
  

  
  
  
  

add a comment | 

1

$begingroup$

ive been trying to derive a mathematical model for the system shown in the image

The case is a pump, pumps water into a Column. The drain of the column is blocked. Thus there is only flow in.

i know i should end up with a differential equation of some order. Which i must solve resulting in an equation for Qin (flow in). The problem is i cannot grasp how to derive the differential equation from the capacitance and resistance of the system.

i know that resistance(fluid) = Change in level difference divided by change in flow rate

and capacitance (fluid) = change in volume of liquid stored/ change in head

Interance is ignored.

Laminar Flow is assumed for now to remove the need to decide between laminar or turbulent flow.

I know that these 2 are the analogy of electrical resistance and capacitance.

An experimental pump voltage and was applied in the lab and a flow rate recorded. Column volume and cross sectional area are know. all the values of the information is supplied in the attached image.

Realy im looking for guidance on deriving differential equations form systems.
Pleas help been starring at this for 10+hours. Dieing internally.

]

mathematical-modeling fluid-dynamics

share|cite|improve this question

edited Mar 22 at 0:54

Alex Chala

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. I don't see how your question has anything to do with modular arithmetic, so why did you use the "modular-arithmetic" tag (About modular-arithmetic gives a description of this tag)?
  $endgroup$
  – John Omielan
  Mar 22 at 0:34
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Apologizes. Thats meant to be mathematical-modeling. Ill try edit it
  $endgroup$
  – Alex Chala
  Mar 22 at 0:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  No worries. Mathematical-modeling makes a lot more sense.
  $endgroup$
  – John Omielan
  Mar 22 at 0:54
  

  
  
  
  

add a comment | 

$begingroup$

ive been trying to derive a mathematical model for the system shown in the image

The case is a pump, pumps water into a Column. The drain of the column is blocked. Thus there is only flow in.

i know i should end up with a differential equation of some order. Which i must solve resulting in an equation for Qin (flow in). The problem is i cannot grasp how to derive the differential equation from the capacitance and resistance of the system.

i know that resistance(fluid) = Change in level difference divided by change in flow rate

and capacitance (fluid) = change in volume of liquid stored/ change in head

Interance is ignored.

Laminar Flow is assumed for now to remove the need to decide between laminar or turbulent flow.

I know that these 2 are the analogy of electrical resistance and capacitance.

An experimental pump voltage and was applied in the lab and a flow rate recorded. Column volume and cross sectional area are know. all the values of the information is supplied in the attached image.

Realy im looking for guidance on deriving differential equations form systems.
Pleas help been starring at this for 10+hours. Dieing internally.

]

mathematical-modeling fluid-dynamics

share|cite|improve this question

edited Mar 22 at 0:54

Alex Chala

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61

$endgroup$

share|cite|improve this question

edited Mar 22 at 0:54

Alex Chala

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61

share|cite|improve this question

edited Mar 22 at 0:54

Alex Chala

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61

asked Mar 22 at 0:16

Alex ChalaAlex Chala

61