To find : weight of steel per metre.
Since the formula to be derived is d^2/162, assumed cross section is circular and the material is cylinder.
Weight density of steel = 7850 kg/m^3.
Weight density = weight/volume.
Weight = weight density x volume.
Volume of cylinder= πh d^2 /4
h is the height of cylinder bar. = 1m
d is diameter in mm
Volume = 3.14/4 x d^2 x 10^-6.(converted mm to m two times for d)
Volume of cylindrical bar = (7.85 x 10^-7) d^2 cum
Weight of cylindrical bar
= 7850 x 7.85 x 10^-7 x d^2.
= 0.00616 x d^2
= d^2 /(0.00616^-1)
Since d’s unit is converted into the formula from mm to m, you can directly use the dia number to find out the weight per metre. For example:
25 mm dia bar:
625/162 = 3.85 kg