Question

A waste treatment pond is 50 m long and 25 m wide, and has an average depth of 2 m. The density of the waste is 75.3lbm/ft^3 .Calculate the weight of the pond contents in lbf ,using single dimensional equation for your calculation.

Answer 1

To calculate the weight of the pond contents, find the volume of the pond and convert it to cubic feet. Then, multiply the volume by the density of the waste to find the weight in pounds-force (lbf).

Step-by-step explanation:

To calculate the weight of the pond contents, we need to first find the volume of the pond. The volume of a rectangular prism is given by V = length x width x height. In this case, the length is 50 m, the width is 25 m, and the average depth is 2 m. So the volume of the pond is 50 m x 25 m x 2 m = 2500 m^3.

Next, we need to convert the volume from cubic meters to cubic feet. Since 1 cubic meter is approximately 35.3147 cubic feet, we can multiply the volume by this conversion factor: 2500 m^3 x 35.3147 ft^3/m^3 = 88,286.75 ft^3.

Finally, to find the weight of the pond contents in pounds-force (lbf), we can multiply the volume in cubic feet by the density of the waste. The density is given as 75.3 lbm/ft^3. So the weight of the pond contents is 88,286.75 ft^3 x 75.3 lbm/ft^3 = 6,648,007.28 lbf.

Answer 2

`W = 6.65 \cdot 10^(6) lbf`

Step-by-step explanation:

To find the weight (W) of the pond contents first we need to use the following equation:

`W = m\cdot g` (1)

Where m the mass and g is the gravity

Also, we have that the mass is:

`m = \rho*V` (2)

Where ρ is the density and V the volume

We cand calculate the volume as follows:

`V = L*w*d` (3)

Where L is the length, w is the wide and d is the depth

By entering equation (2) and (3) into (1) we have:

`W = \rho*L*w*d*g`

`W = 75.3 lbm/ft^(3)*50 m*25 m*2 m*9.81 m/s^(2)`

`W = 75.3 lbm/ft^(3)*((1 ft)^(3))/((0.3048 m)^(3))*(0.454 kg)/(1 lbm)*50 m*25 m*2 m*9.81 m/s^(2) = 2.96 \cdot 10^(7) N}*(0.2248 lbf)/(1 N) = 6.65\cdot 10^(6) lbf`

Therefore, the weight of the pond is 6.65x10⁶ lbf.

I hope it helps you!