In the hydraulic system shown in the figure, the piston on the left has a diameter of 4.5cm and a mass is 3.0kg.
If the density of the fluid is 710kg/m^3 , what is the height difference h between the two pistons in m?
I checked the other similar questions like this and tried to solve the question using the
Pressure (P) = pgh, but still could not get the right answer. the answer I got was 1.6
To find the height difference between the two pistons, we can use the principle of Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.
First, let's find the pressure exerted by the piston on the left. We can use the formula:
Pressure (P) = Force (F) / Area (A)
The force exerted by the piston on the left can be calculated as the product of its mass (m) and the acceleration due to gravity (g). Since it is in equilibrium, the force applied by the fluid on the right piston will be the same.
Force (F) = mass (m) * acceleration due to gravity (g)
Given:
Mass (m) = 3.0 kg
Acceleration due to gravity (g) = 9.8 m/s²
F = 3.0 kg * 9.8 m/s²
F = 29.4 N
The area of the piston is given by the formula:
Area (A) = π * radius²
Since the diameter of the piston is given, we can calculate the radius using the formula:
Radius (r) = diameter / 2
Given:
Diameter = 4.5 cm = 0.045 m
r = 0.045 m / 2
r = 0.0225 m
Now, we can calculate the area:
A = π * (0.0225 m)²
A ≈ 0.00159 m²
Now, we can find the pressure:
P = F / A
P = 29.4 N / 0.00159 m²
P ≈ 18413.84 Pa
Since the pressure is transmitted equally in all directions, the pressure exerted by the fluid on the right piston is also 18413.84 Pa.
Now, we can find the height difference (h) between the two pistons using the formula:
Pressure (P) = density (ρ) * gravity (g) * height difference (h)
Given:
Density (ρ) = 710 kg/m³
Gravity (g) = 9.8 m/s²
Plugging in the values, we have:
18413.84 Pa = 710 kg/m³ * 9.8 m/s² * h
h = 18413.84 Pa / (710 kg/m³ * 9.8 m/s²)
h ≈ 2.42 m
Therefore, the height difference (h) between the two pistons is approximately 2.42 meters.