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

Verified Answer :

a386

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)