Will the Water Level Decrease When Ice Cubes Melt?

[tronter]

Homework Statement

Lets say the density of water is $$\rho_{water}$$ and the density of ice is $$\rho_{ice} < \rho_{water}$$. When the ice cubes melt, does the water level stay the same, increase, or decrease?

Homework Equations

$$P = P_0 + \rho_{w} g d$$

$$P_1 + \frac{1}{2}\rho v_{1}^{2} + \rho g y_1 = P_2 + \frac{1}{2}\rho v_{2}^{2} + \rho g y_2$$

The Attempt at a Solution

I know intuitively that the water level will decrease. To use the equations to prove this fact, I should maybe consider a cup of height $$h$$ with ice cubes, and then apply the equations?

Thanks

 

[Mentz114]

What are those formulae ? They look like Bernoulli equations which are not relevant here. You need buoyancy. If you model the situation specify the dimensions of the glass and the ice cube because they matter.