Answer:
The Gauge pressure at 9 meters depth is [tex]150 \, kPa[/tex]
Explanation:
Gauge pressure is the difference between absolute pressure and some reference pressure, most commonly atmospheric pressure. The increment in pressure caused by a static fluid is given by:
[tex]\Delta P = \rho g d[/tex] where [tex]\rho[/tex] is the density of the liquid, g is the accleration due to gravity and d is the depth.
Now, we see that [tex]\Delta P[/tex] is linearly proportional to d, and we can assume that [tex]\rho[/tex] remains constant, because liquids are usually not compressible.
Given that the greater depth is simply 3 times the smaller depth:
[tex]d_2=3\cdot d_1\\9\,m= 3 \cdot 3\,m[/tex]
[tex]\Delta P[/tex] at [tex]9\, m[/tex] of depth will also be three times the gauge pressure at [tex]3 \,m[/tex] of depth.
We could also have calculated [tex]\rho[/tex] ny using:
[tex]\Delta P = \rho \,g \,d\\\\\rho = \frac{\Delta P}{g \, d}\\\\\rho = \frac{\Delta P}{g \, d}= \frac{30 \,kPa}{9.8 \frac{m}{s^2} \, 3\,m}=1020.41 \frac{kg}{m^3}[/tex]
and used this result to calculate the gauge pressure. These are both similar methods that yield the same result
