Casting: Problem Solving

P $1$ The flow rate of liquid metal into the downsprue of a mold $=1\frac{L}{s}.$ The cross$-$sectional area at

the top of the sprue $=800mm2,$ and its length $=175mm.$ What area should be used at the base of

the sprue to avoid aspiration of the molten metal?

P $2$ A cylindrical riser must be designed for a sand$-$casting mold. The casting itself is a steel

rectangular plate with dimensions $7\mathrm{.}5cm12\mathrm{.}5cm2\mathrm{.}0cm.$ Previous observations have indicated

that the total solidification time $($TTS$)$ for this casting $=1\mathrm{.}6$min. The cylinder for the riser will

have a diameter$-$to$-$height ratio $=1\mathrm{.}0.$ Determine the dimensions of the riser so that its TTS $=2\mathrm{.}0$

min.

P $3$ A riser in the shape of a sphere is to be designed for a sand casting mold. The casting is a

rectangular plate, with length $=200mm,$ width $=100mm,$ and thickness $=18mm.$ If the total

solidification time of the casting itself is known to be $3\mathrm{.}5$ min $,$ determine the diameter of the riser

so that it will take $25\%$ longer for the riser to solidify.

P $4$ A horizontal true centrifugal casting process is used to make brass bushings with the following

dimensions: length $=10cm,$ outside diameter $=15cm,$ and inside diameter $=12cm.($a$)$ Determine

the required rotational speed in order to obtain a G$-$factor of $70.($b$)$ When operating at this speed,

what is the centrifugal force per square meter $($ Pa $)$ imposed by the molten metal on the inside wall

of the mold?

Solve all please