Thermal expansion of oil overflowing from a tank

[Doct3r88]

Homework Statement

A waste handling machine requires a cube shaped steel oil tank of side length 100mm to be designed which will be subject to a fluid pressure of 80MN/m². The oil tank as an overflow valve fitted to the top of the tank, the tank is completely filled with oil at an optimum operating temperature of 50°C, under your investigations in the R&D dept it was found that the oil temperature could rise to 78°C depending on the operating time and external environmental temperature. Ignoring the fluid pressure, determine how much oil will overflow from the tank. Take the volumetric coefficient of expansion of the oil as 764 x 10-6 °C -1 and the linear coefficient of expansion of steel as 12 x 10-6 °C -1.

Relevant Equations

∆L=αL_0 ∆T
δV_o=V_o*β*∆T

Just wanted to know if I was barking up the wrong bush or not with my working out if anyone could help?

 

[.Scott]

You are multiplying the volumetric expansion of the oil by 3. I am not sure why.
It the intention is to convert it from a linear expansion to a volumetric expansion, then it is wrong, because at the bottom of page 1 you are defining it ( $a_0$ ) to be volumetric already.

 

[Doct3r88]

Ah yes I see what you're saying I think I misread the example given and to go from linear to volumetric I would have had to multiply by 3 thank you. Amended now to get 20.3717mm^3*10^-3.

My doubt was over whether I had gone about working out the expansion of the steel tank correctly or whether I should have converted the steel linear expansion into volumetric then subtracted them from one another.