Answer:
The approximate mass of the weight required is 348.3 kg
Explanation:
The dimensions of the dead-weight gauge are;
The pressure up to which the dead-weight gauge measures, P = 3,000 bar
The diameter of the piston of the dead-weight gauge, D = 4 mm = 0.004 m
The dead-weight gauge pressure formula is given as follows;
Pressure, P = The weight applied, W ÷ The area the weight is applied, A
∴ The weight applied, W = P × A
Where;
P = Pressure
A = The area the weight is applied
W = The weight applied to the piston
The area the weight is applied, A = The area of the piston = π·D²/4
Where;
D = The diameter of the piston
∴ A = π × (0.004 m)²/4
When P = 3,00 bar, and A = π × (0.004 m)²/4, we have;
The weight applied, W = P × A
∴ W = 3,000 × π × (0.004 m)²/4 ≈ 3,769.9118 N
W ≈ 3,769.9118 N
W = m·g
Where;
m = The mass of weight
g = The acceleration due to gravity ≈ 9.81 m/s²
m = W/g
∴ m = 3,769.9118 N/(9.81 m/s²) ≈ 384.3 kg
The approximate mass of the weight required, m = 348.3 kg.
We started by Solving for the force and then the area of the piston, we then applied the formula for force using the constant for acceleration due to gravity and the mass was found to be 384.34 kg
Given Data
Pressure = 3000 bar
Diameter = 4mm
Let us convert bar to N/mm^2
1 bar = 0.1 N/mm^2
3000 bar = x N/mm^2
= 0.1*3000
= 300 N/mm^2
We know that pressure P = Force/Area
Let us find the area of the piston
Area = πd^2/4
Area = 3.142*4^2/4
Area = 3.142*16/4
Area = 50.272/4
Area = 12.568 mm^2
Let us find the force F
F = P*Area
F = 300*12.568
F = 3770.4 Newton
We know that Force = Mg
g = 9.81 m/s^2
Hence, m = F/g
m = 3770.4/9.81
m = 384.34 kg
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