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.
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