A liquid has a volume of 2000 cm³ and a mass of 24 kg. Calculate the height of the column of the liquid that exerts a pressure of 3600 N/m². The length of the side is 20 cm by 5 cm.
Answer (2)
To determine the height of a liquid that exerts a pressure of 3600 N/m², we calculated the liquid density and used the pressure formula. The height of the liquid column is approximately 3.06 cm. This is derived using the pressure equation and the density of the liquid based on its mass and volume.
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To calculate the height of the column of liquid that exerts a specified pressure, we can use the hydrostatic pressure formula:
P = ρ ⋅ g ⋅ h
Where:
P is the pressure exerted by the liquid (3600 N/m²).
ρ is the density of the liquid (in kg/m³).
g is the acceleration due to gravity (approximately 9.81 m/s²).
h is the height of the liquid column (in meters).
First, we need to calculate the density ρ of the liquid. Density is mass divided by volume:
ρ = volume mass = 2000 cm 3 24 kg
We need to convert the volume from cm³ to m³:
2000 cm 3 = 2000 × 1 0 − 6 m 3 = 0.002 m 3
So, the density of the liquid is:
ρ = 0.002 24 = 12000 kg/m 3
Now, using the hydrostatic pressure formula to find the height:
3600 = 12000 × 9.81 × h
Solving for h :
h = 12000 × 9.81 3600
h ≈ 117720 3600 ≈ 0.0306 m
Therefore, the height of the liquid column is approximately 0.0306 meters or 3.06 cm.
