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jonny [76]
3 years ago
13

The depth of water behind the Hoover Dam is 220 m. Find the water pressure at the base of this dam.

Physics
1 answer:
Sav [38]3 years ago
6 0
Pressure under water is called the gauge pressure.
Pressure= \frac{Force}{Area}  \\ F=mg \\ P= \frac{mg}{A}
Now the next part is difficult to put into an equation because you need the symbol for density, which is ρ, pronounced rho.  I cannot type ρ into the equation so I will use p.
p= \frac{m}{V} (m=mass, V=Volume)
m=pV \\ P=  \frac{pVg}{A}  \\ V=Ah
A=Area of the base of the object, or cylinder of water above the object, h= height of object
P= \frac{p(Ah)g}{A}
The "A"s cancel, leaving us with
P=pgh

You are only looking for the water pressure, so you would not be concerned with atmospheric pressure on top of that.

P_{gauge} =p_{liquid} g h_{object}

The density of water is 1000 \frac{kg}{ m^{3} }
Use 1000 for ρ
Gravity is 9.8
Height is 220

P=pgh \\ P=1000*9.8*220 \\ P=2.16*10^{6} Pa
(Pa is Pascals, the unit for pressure)
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