Here is a demonstration Pascal used to show the importance of a fluid's pressure on the fluid's depth(Figure 1) : An oak barrel with a lid of area 0.17m2 is filled with water. Along, thin tube of cross-sectional area 5.0×10−5m2 is inserted into a hole at the center of the lid, and water is poured into the tube. When the water reaches 12 m high, the barrel bursts.
What was the weight of the water in the tube?
What was the pressure of the water on the lid of the barrel?
What was the net force on the lid due to the water pressure?
500 N
To find the weight of the water in the tube, we need to first find the volume of water in the tube by multiplying the height of the water column by the cross-sectional area of the tube.
Volume of water in the tube = Height of water column × Cross-sectional area of the tube
In this case, the height of the water column is given as 12 m, and the cross-sectional area of the tube is given as 5.0×10^(-5) m².
Volume of water in the tube = 12 m × 5.0×10^(-5) m²
To calculate the weight of the water in the tube, we need to multiply the volume of water in the tube by the density of water. The density of water is approximately 1000 kg/m³.
Weight of water in the tube = Volume of water in the tube × Density of water
Weight of water in the tube = (12 m × 5.0×10^(-5) m²) × 1000 kg/m³
To find the pressure of the water on the lid of the barrel, we can use Pascal's principle, which states that the pressure exerted by a fluid is transmitted equally in all directions. Therefore, the pressure on the lid will be the same as the pressure at the bottom of the water column.
Pressure = Force / Area
The force exerted by the water is equal to the weight of the water in the tube, and the area is given as 0.17 m².
Pressure on the lid = Weight of water in the tube / Area of the lid
Pressure on the lid = (12 m × 5.0×10^(-5) m² × 1000 kg/m³) / 0.17 m²
Finally, to find the net force on the lid due to the water pressure, we can use the formula:
Net force = Pressure × Area
Net force on the lid = Pressure on the lid × Area of the lid
Net force on the lid = [(12 m × 5.0×10^(-5) m² × 1000 kg/m³) / 0.17 m²] × 0.17 m²