A tank 4m long ,3m wide and 2m deep is filled to the brim with paraffin of density 800kg/mg (a) calculate the pressure on the base of the tank (b) calculate the force acting on the base
Given the dimensions of the tank, we can calculate the volume of the tank first:
Volume = length × width × depth = 4m × 3m × 2m = 24 m³.
The mass of paraffin can be calculated using the density:
Density = mass/volume
Mass = Density × volume = 800 kg/m³ × 24 m³ = 19200 kg
The weight of the paraffin can be calculated as:
Weight = mass × gravitational acceleration (g) = 19200 kg × 9.81 m/s² ≈ 188352 N.
The pressure on the base of the tank can be calculated using the formula:
Pressure = Force/Area. Since the weight of the paraffin is acting on the base, the force here is its weight.
The area of the base is given by length × width = 4m × 3m = 12m².
Pressure = Force/Area = 188352 N / 12 m² ≈ 15696 Pa. (a)
To calculate the force acting on the base, we can use the formula:
Force = Pressure × Area = 15696 Pa × 12m² ≈ 188352 N. (b)
So, the pressure on the base of the tank is about 15.696 kPa, and the force acting on the base is about 188.352 kN.
To calculate the pressure on the base of the tank, we can use the formula:
Pressure = Density x Gravity x Height
(a) Pressure on the base of the tank:
Given:
Density of paraffin = 800 kg/m^3
Height of the tank = 2 m
Gravity = 9.8 m/s^2 (approximate value)
Using the formula, we can calculate the pressure:
Pressure = (800 kg/m^3) x (9.8 m/s^2) x (2 m)
Pressure = 15680 Pascal (Pa)
So, the pressure on the base of the tank is 15680 Pa (or N/m^2).
(b) To calculate the force acting on the base of the tank, we can use the formula:
Force = Pressure x Area
Given:
Length of the tank = 4 m
Width of the tank = 3 m
Using the formula and the pressure calculated earlier, we can calculate the force:
Force = 15680 Pa x (4 m x 3 m)
Force = 188160 Newtons (N)
So, the force acting on the base of the tank is 188160 N.
To calculate the pressure on the base of the tank, we can use the formula:
Pressure = Density * gravity * height
where:
Density = 800 kg/m^3 (density of paraffin)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Height = 2 m (depth of the tank)
(a) Calculate the pressure on the base of the tank:
Pressure = Density * Gravity * Height
= 800 kg/m^3 * 9.8 m/s^2 * 2 m
= 15,680 Pa
Therefore, the pressure on the base of the tank is 15,680 Pa.
To calculate the force acting on the base, we can use the formula:
Force = Pressure * Area
where:
Pressure = 15,680 Pa (calculated in part a)
Area = Length * Width
(b) Calculate the force acting on the base:
Area = Length * Width
= 4 m * 3 m
= 12 m^2
Force = Pressure * Area
= 15,680 Pa * 12 m^2
= 188,160 N
Therefore, the force acting on the base of the tank is 188,160 Newtons.