In the field of engineering a ‘water model’ is often used to explain electricity

Question

In the field of engineering a ‘water model’ is often used to explain electricity, with pressure replacing potential and volumetric flow rate replacing current. Answer the following: Explain all answers & show all work.

a) What is volumetric flow rate and what are its units in both SI and English units?

b) in the water model above what are the SI units of volumetric current density. (Take note of its units)

c) If you double the hole size (of a leak) in a big tank what happens to the volumetric flow rate of the leak? From Bernoulli eq. we know the velocity v of a leak in hole in the bottom of a tank of height h is given by v = 2gh

d) What happens to the volumetric current. density (when hole size is doubled). Compare to current density behavior in 1c).

Explanation / Answer

a) Volumetric flow rate is the volume of the liquid which passes per unit time.

SI units m3/s , English units : ft3/s or gallons per minute.

b) Coloumbs / m3

c) If you double the size of the hole, i.e the area of the hole (assuming circular) will increase to four times, the resistance to the flow will decrease to one fourth , Since flow rate is F= delta P/R , flow rate will also increase by one fourth

d) As the size of the conductor is doubled i.e radius of circular wire is doubled , the cross section area increses by 4 times and the resistance decreases to one fourth of initial value. Therefore as the size increases current will increase to one fourth

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