Question

A closed cylindrical tank 2.4m in diameter and 7.5 m long is completely filled with gasoline, of specific gravity 0.90. The tank, with its long axis horizontal is pulled by a truck along a horizontal surface.

a. Determine the pressure difference between ends along the axis of the tank when the truck undergoes an acceleration of 1.5m/s^2. (Ans. 10.125 kpa)
b. Determine the total force on the rear wall (Ans. 93.7 kN)

Answer 1

The pressure difference between the ends along the axis of the tank when the truck undergoes an acceleration of 1.5 m/s² is 10.125 kPa. The total force on the rear wall of the tank is 183.375 kN.

Step-by-step explanation:

To determine the pressure difference between the ends along the axis of the tank when the truck undergoes an acceleration of 1.5 m/s², we can use the equation:

Pressure difference = Density × Acceleration × Length

Since the tank is filled with gasoline, which has a specific gravity of 0.9, the density of gasoline can be calculated as:

Density = Specific gravity × Density of water

Plugging in the values, we have:

Density = 0.9 × 1000 kg/m³

Substituting this into the pressure difference formula, we get:

Pressure difference = (0.9 × 1000 kg/m³) × (1.5 m/s²) × (7.5 m) = 10125 Pa

Therefore, the pressure difference between the ends along the axis of the tank when the truck undergoes an acceleration of 1.5 m/s² is 10.125 kPa.

In order to determine the total force on the rear wall of the tank, we can use the equation:

Force = Pressure × Area

The area of the rear wall can be calculated as the product of the diameter and length of the tank:

Area = π × (2.4 m)²

Plugging in the values, we have:

Area = 3.14 × (2.4 m)² = 18.10 m²

Substituting this into the force formula, we get:

Force = (10125 Pa) × (18.10 m²) = 183375 N

Therefore, the total force on the rear wall of the tank is 183.375 kN.

Answer 2

The pressure difference between the ends of the tank is 10.125 kPa, and the total force on the rear wall is 93.7 kN.

Step-by-step explanation:

To determine the pressure difference between the ends of the tank, we can use the equation:
Pressure = Density x Acceleration x Height

Given that the tank is filled with gasoline of specific gravity 0.90, the density can be calculated as:
Density = Specific Gravity x Density of Water

Substituting the given values into the equation, we get:
Pressure = 0.90 x 1000 kg/m^3 x 1.5 m/s^2 x 7.5 m
Simplifying the equation gives a pressure of 10.125 kPa.

To determine the total force on the rear wall of the tank, we can use the equation:
Force = Pressure x Area

Substituting the given values into the equation, we get:
Force = 10.125 kPa x (π x (1.2 m)^2)
Simplifying the equation gives a force of 93.7 kN.