Determining weight without using weighing scales

Many people would think of using weighing scales when they are asked to determine the weight of something. That may be applicable in small scale but when it comes to heavy structural load computations, we need a mathematical approach and that is what I'll discuss in this blog.

Determining weight by volume

The ratio of mass over volume is called density. The value of density varies among material types. Density is basically weight per volume unit (e.g. kg/cubic meter).

From the relation,

D = M / V

where:
D = Density
M = Mass
V = Volume

we can get the Mass by multiplying the Volume to the known Density.

M = D V

Example:

Determine the total weight of 1.5m diameter by 2.5m high 3mm thick cylindrical water tank at full capacity. The bottom of the tank is 4mm thick and the top cover is 3mm thick.

Solution:

I. Determining the volumes
The first step is to calculate the volumes the tank and the content. The formula for volume of cylinder is

V = πdh

where:

V = Volume
π = pi = 3.1416
h = height

A. Total volume
VT = π(1.5m)(2.5m)
VT = 11.781 cubic meters

B. Volume of water
VW = π(1.494m)(2.493m)
VW = 11.701 cubic meters

C. Volume of tank
Vtank = VT - VW
Vtank = 0.08 cubic meters


I. Determining the weights
To get the weights of water and tank, multiply the volume by the density. The density of water is 1000 kg / cu.m and the density of steel is 7850 kg / cu.m.

A. Weight of Water
Ww = VW x 1000 kg/cu.m
Ww = 11.701cu.m x 1000kg/cu.m
Ww = 11701 kg or 11.7 tons

B. Weight of tank
Wtank = Vtank x 7850 kg/cu.m
Wtank = 0.08 cu.m x  7850 kg/cu.m
Wtank = 638 kg or 0.638 tons

C. Total weight
WT = Ww + Wtank
WT = 11.701 tons + .638 ton
WT = 12.339 tons