1. Pressures up to 3000 bar are measured with a dead-weight gauge. The piston diameter is 4 mm. What is the approximate mass in kg of the weights required

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.