Problem $2(30$ points$)$:

A two$-$piece pattern for the spool shown in the accompanying figure is to be sand cast out of

an aluminum casting alloy. A cross$-$sectional view of one$-$half of the spool when placed in the

drag is also provided to indicate the projected mold$-$cavity area at the parting plan.

Given:

Density of molten casting alloy $=2750$kg$//$m$^(3)$

Density of sand used $=400$kg$//$m$^(3)$

The cope and drag are $500$ mm in height

The sketch casting pattern for the spool

A cross$-$sectional view of one$-$half of the spool

a$)$ If the height of the sprue can be assumed to be equal to the height of the cope, determine

the velocity of the liquid aluminum at the bottom of the sprue $(8$ Points$)$

b$)$ Determine the cross$-$section area of the gate $($which can be assumed to be the same as

bottom of the sprue$)$ if the flow rate of $1000$cm$^(3)//$s is to be maintained. $(8$ points$)$

c$)$ The mold filling time if the flow rate of $1000$cm$^(3)//$s is to be maintained. Ignore the liquid

in the sprue and runners. $(7$ points$)$

d$)$ To save costs no clamping mechanism is allowed. If the width and length of rectangular

cope are equal, find the dimensions $($i$.$e$.$ the width and length$)$ of the cope required to cast

the part without the need for clamping. Ignore the weight of the flask $(7$ Points$)$