One can come to understand the hydrostatic principles by working a number of varied problems. Casting Railcar Wheels is another illustration of technique.

Casting Railcar Wheels The apparatus is used to cast steel into wheels for railroad cars. The process begins by placing a large "ladle" of molten steel in a chamber, then covering it with a heavy air-tight lid. Ceramic wheel molds are arranged on top each with a "refractory tube" or pipe that extends downward into the molten steel.

Once set up, casting happens as nitrogen is injected slowly into the chamber. As the nitrogen pressure increases the surface of the liquid steel in the ladle is pushed down and molten steel flows up the "refractory tubes" into the wheel molds. The liquid fills the mold, next fills the "gas vent" ports and ultimately, flows to a small puddle on top of the mold. It is known that the mold is full when molten steel issues from the "gas vent." The ladle has enough steel to cast 6 wheels. The depth of steel in the ladle is 1.8 meters. It is circular and has an average diameter of 2.5 meters. What mass of steel is forced out of the ladle? Also, what maximum pressure must the chamber withstand?

♦  This problem involves liquid steel and gaseous nitrogen.

We inspect the physical arrangement to find a place where we know (can reasonably state) the pressure. When liquid steel flows out on top of the mold, its pressure will be 1 atmosphere (a). Also, this being the end of the cast, the level of steel in the ladle will be at its bottom (b). That condition will correspond to the maximum pressure of the nitrogen.

We construct a hydrostatic equation containing the gage reading, GR. Begin at point (a) where the pressure is known to be one atmosphere. The proceed down in the liquid steel to (b). The pressure at (b) will be:

p_atm + ρ_steel  g_o(2.8m) = p_b

Next, we imagine the pressure change as our point moves up 1.8 meters through nitrogen to the gage, then through the gage to the atmosphere.

p_atm + ρ_steel  g_o(2.8m) - ρ_Nitrogeng_o(1.8m) - G.R. = p_atm

Our answer is at hand, except we don't know the know the density of the nitrogen. To proceed, we assume the contribution of the nitrogen is negligibly small.