Answer :
Final answer:
The volume of a bluefin tuna that weighs 290 kg and is submerged at a depth where the absolute pressure is 251,700 Pa can be calculated using buoyancy principles, resulting in approximately 0.283 cubic meters.
Explanation:
To find the volume of the bluefin tuna, we can apply Pascal's principle and the concept of absolute pressure in fluids. The absolute pressure at a depth of 15 meters in water reflects the pressure from the weight of the water above, in addition to the atmospheric pressure at the surface.
The formula to calculate absolute pressure at a certain depth is:
P = P0 + ρgh
Where:
- P is the absolute pressure at depth
- P0 is the atmospheric pressure at sea level
- ρ (rho) is the density of the fluid (sea water)
- g is the acceleration due to gravity
- h is the depth below the surface
However, since the absolute pressure at the fish's depth is already provided (251,700 Pa), we do not need to calculate it. The excess pressure (gauge pressure) can be found by subtracting the atmospheric pressure from the absolute pressure:
Pgauge = P - P0
Then, using the principle of buoyancy, we know that the buoyant force on the fish must be equal to the weight of the volume of water displaced by the fish. This can be expressed as:
Fbuoyant = V ρg
Where V is the volume of the fish.
The weight of the fish is also equal to the product of its mass and gravity:
W = mg
Equating the buoyant force to the weight, we have:
V ρg = mg
And hence the volume V is:
V = m/ρ
Since ρ is the density of sea water and it is typically about 1025 kg/m³, and the mass m of the fish is 290 kg, we can plug in these values to compute the volume:
V = 290 kg / 1025 kg/m³
So the volume of the fish is approximately:
V ≈ 0.283 m³
