If a tank filled with water contains a block and the height of the water above point A within the block is 0.6 meter, what’s the pressure at point A?
The Correct Answer and Explanation is:
To find the pressure at point A, we use the hydrostatic pressure formula:P=ρghP = \rho g hP=ρgh
Where:
- PPP = pressure at the point (in Pascals, Pa)
- ρ\rhoρ = density of water (typically 1000 kg/m31000 \, \text{kg/m}^31000kg/m3)
- ggg = acceleration due to gravity (approx. 9.81 m/s29.81 \, \text{m/s}^29.81m/s2)
- hhh = height of water above the point (in meters)
Given:
- h=0.6 mh = 0.6 \, \text{m}h=0.6m
- ρ=1000 kg/m3\rho = 1000 \, \text{kg/m}^3ρ=1000kg/m3
- g=9.81 m/s2g = 9.81 \, \text{m/s}^2g=9.81m/s2
Calculation:
P=1000×9.81×0.6=5886 PaP = 1000 \times 9.81 \times 0.6 = 5886 \, \text{Pa}P=1000×9.81×0.6=5886Pa
Final Answer: 5886 Pascals (Pa)
Explanation
Pressure in a fluid increases with depth due to the weight of the fluid above. This principle is described by the hydrostatic pressure formula P=ρghP = \rho g hP=ρgh, where pressure is directly proportional to the depth of the fluid (hhh), the fluid’s density (ρ\rhoρ), and gravitational acceleration (ggg).
In this problem, point A is located inside a block submerged in water. The pressure at point A depends solely on how much water is above it — that is, the height of the water column above point A. This is because pressure in a fluid at rest is determined by the vertical depth and not by the shape or orientation of the container or object.
Since the height of water above point A is 0.6 meters, we calculate the pressure using the standard values for water’s density (1000 kg/m³) and gravity (9.81 m/s²). Multiplying these with the height gives us:P=1000×9.81×0.6=5886 PaP = 1000 \times 9.81 \times 0.6 = 5886 \, \text{Pa}P=1000×9.81×0.6=5886Pa
This result means that every square meter at point A experiences a force of 5886 Newtons due to the weight of the water above. Notably, the pressure at a given depth in a fluid is the same regardless of the container or whether a solid object is present. Therefore, even though point A is within a block, as long as it is submerged and exposed to the water, the hydrostatic pressure still applies.
This fundamental concept is essential in fluid mechanics and is widely used in engineering, meteorology, and even medicine.Tools
