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Zorluk: ZorHydrostatic Pressure

An industrial processing facility uses two large vertical storage tanks that are open to the atmosphere. Tank A contains two distinct layers of non-mixing liquids: a 5-meter5\text{-meter} top layer of oil (density = 800 kg/m3800\text{ kg/m}^3) and a 3-meter3\text{-meter} bottom layer of water (density = 1000 kg/m31000\text{ kg/m}^3). Tank B, which has exactly twice the cross-sectional area of Tank A, contains pure water to a total depth of 8 meters8\text{ meters}. Which of the following statements correctly compares the gauge hydrostatic pressure acting on the interior bottom surfaces of the two tanks?

  1. A
    The pressure at the bottom of Tank B is greater primarily because its larger cross-sectional area holds a much larger total volume and weight of fluid.
  2. B
    The pressures are exactly equal because the total depth of the fluid column is 8 meters8\text{ meters} in both tanks, regardless of the container's base area.
  3. The pressure at the bottom of Tank B is greater because the entire 8-meter8\text{-meter} fluid column consists of the denser liquid.Cevap
  4. D
    The pressure at the bottom of Tank A is greater because the oil layer physically compresses the water layer below it, multiplying the downward force.

Cevap

The pressure at the bottom of Tank B is greater because its entire fluid column is composed of the denser water, yielding a higher hydrostatic pressure than Tank A's mixed column.
The correct answer accurately calculates that Tank B has a higher bottom pressure because it contains a full 8-meter8\text{-meter} column of the denser water (1000 kg/m31000\text{ kg/m}^3), while Tank A replaces 5 meters5\text{ meters} of that column with lighter oil (800 kg/m3800\text{ kg/m}^3). It also correctly implies that hydrostatic pressure depends only on fluid density and depth, not on the tank's cross-sectional area.

Adım Adım Çözüm

1
Identify the formula for gauge hydrostatic pressure.
The hydrostatic pressure PP at a depth hh is calculated using P=ρghP = \rho gh, where ρ\rho is the fluid density and gg is the acceleration due to gravity.
This formula is needed to find the pressure at the bottom of each tank.
2
Calculate the relative pressure at the bottom of Tank A.
For multiple layers, sum the individual pressures: PA=(ρoil×g×hoil)+(ρwater×g×hwater)=(800×g×5)+(1000×g×3)=4000g+3000g=7000g PaP_A = (\rho_{oil} \times g \times h_{oil}) + (\rho_{water} \times g \times h_{water}) = (800 \times g \times 5) + (1000 \times g \times 3) = 4000g + 3000g = 7000g\text{ Pa}.
The total bottom pressure in a multi-fluid system is the combined pressure of all stacked fluid layers.
3
Calculate the relative pressure at the bottom of Tank B.
Tank B contains only water: PB=ρwater×g×htotal=1000×g×8=8000g PaP_B = \rho_{water} \times g \times h_{total} = 1000 \times g \times 8 = 8000g\text{ Pa}.
This calculation provides the value needed to compare Tank B against Tank A.
4
Compare the pressures and analyze the effect of tank width.
Since 8000g>7000g8000g > 7000g, Tank B has the higher bottom pressure. The larger cross-sectional area of Tank B is irrelevant to the calculation.
Hydrostatic pressure depends solely on depth and density, meaning a wider container does not artificially increase pressure.

Anahtar Kavram

Hydrostatic pressure depends strictly on fluid density, gravity, and depth (P=ρghP = \rho gh), and is independent of the container's shape, base area, or total volume of fluid.
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Hydrostatic Pressure

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