I would love some help one this I am pretty sure the calculation I need is
KE = 1/2mv2
I have the density of air given as
1.2kg.m-3
I believe I have to assume water is 100x more dense :. I have calculated this;
1.2kg x 1000 = 1200kg.m-3
200kg x 5.6ms2
18816 kg⋅m2⋅s−2 = 18816 joule
...this doesn't look right??? I would really appreciate some help
your equation is correct but I have no idea how you got the density of air into this and why would water be 100 x denser than air? - this would totally depend on the pressure... but you don't need that anyway.
you just need the equation for the kinetic energy: E = mv²/2
now, since you want to have the energy density in J/m³ you should calculate everything in SI units.
hence: 20 km/h = 20/3.6 m/s = 8.33 m/s = v
as the energy density is already in J/m³ just take the mass of one m³ of water and insert it into the energy equation and you are done.
Note, you have to find energy density (and not energy) of the flowing water body.
Assuming the energy E comes from its kinetic motion alone,
E = (1/2) x m x v^2
Divide both sides by volume units l^3 to obtain energy-density, U,
U = E/l^3 = (1/2) x (m/l^3) x v^2
= (1/2) x ρ x v^2; here ρ is the density of water.
= (1/2) x 1000 x 5.55556^2; here v = 20 km/hour = 5.55556 meters/second, and ρ = 1000 kg/m3 is the density of water. Every physical quantity must have values in same metric system, in this case, SI units.
= 0.5 x 1000 x 30.8641
= 15432.067 Joules/m3
ups, I have a correction to make - I miscalculated, sorry: 20 km/h are indeed 5.56 m/s and not 8.33 what I wrote above.
Thank you for your help. I had a lot of typos in my question
Density of water ≈1000 x density of air (1.2 kg/m^3 x 1000 =1200kg/m^3)
(0.5 x 1200kg/m^3) x 5.6ms^2
=18816 Joule/m^3
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