Answer:
1113kN
Explanation:
The ouside diameter OD of the pipe is 61cm and the thickness T is 0.9cm, so the inside diameter ID will be:
Inside Diameter = Outside Diameter - Thickness
Inside Diameter = 61cm - 0.9cm = 60.1cm
Converting this diameter to meters, we have:
[tex]60.1cm*\frac{1m}{100cm}=0.601m[/tex]
This inside diameter is useful to calculate the volume V of water inside the pipe, that is the volume of a cylinder:
[tex]V_{water}=\pi r^{2}h[/tex]
[tex]V_{water}=\pi (\frac{0.601m}{2})^{2}*120m[/tex]
[tex]V_{water}=113.28m^{3}[/tex]
The problem gives you the water density d as 1.0kg/L, but we need to convert it to proper units, so:
[tex]d_{water}=1.0\frac{Kg}{L}*\frac{1L}{1000cm^{3}}*(\frac{100cm}{1m})^{3}[/tex]
[tex]d_{water}=1000\frac{Kg}{m^{3}}[/tex]
Now, water density is given by the equation [tex]d=\frac{m}{V}[/tex], where m is the water mass and V is the water volume. Solving the equation for water mass and replacing the values we have:
[tex]m_{water}=d_{water}.V_{water}[/tex]
[tex]m_{water}=1000\frac{Kg}{mx^{3}}*113.28m^{3}[/tex]
[tex]m_{water}=113280Kg[/tex]
With the water mass we can find the weight of water:
[tex]w_{water}=m_{water} *g[/tex]
[tex]w_{water}=113280kg*9.8\frac{m}{s^{2}}[/tex]
[tex]w_{water}=1110144N[/tex]
Finally we find the total weight add up the weight of the water and the weight of the pipe,so:
[tex]w_{total}=w_{water}+w_{pipe}[/tex]
[tex]w_{total}=1110144N+2500N[/tex]
[tex]w_{total}=1112644N[/tex]
Converting this total weight to kN, we have:
[tex]1112644N*\frac{0.001kN}{1N}=1113kN[/tex]
