2. In the field of engineering a ‘water model’ is often used to explain electric

Question

2. 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

SI units are cubic meter per second

English units are cubic feet per second or gallons per minute

b) Units of volumetric current density is m^3/sec

c) Volumetric flow rate is dV/dt = A*v

A is the area of cross section of the hole

if we double the hole size then i.e radius increases by twice and A increases by 4 times hence the volumetric flow rate is also increases by 4 times

d) volumetric current density also increases by 4 times since volumetric current density is also proportional to area of cross section

volumetric current density = dm/dt = rho*A*v

rho is the density of water

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