Pure aluminum is poured into a sand mold. The metal level in the pouring basin is 10 in. above the metal level in the mold, and the runner is circular with a 0.4-in. diameter. What are the velocity and rate of the flow of the metal into the mold? Is the flow turbulent or laminar? 10.44 A cylinder with a diameter of 1.5 in. and height of 3 in. solidifies in 3 minutes in a sand casting operation. What is the solidification time if the cylinder height is doubled? What is the time if the diameter is doubled?

Solution :

Given :

Height at which the metal is poured, h = 10 in

Diameter of the runner , d = 0.4 in

Assume viscosity, μ = 0.004 Pa-s

Now considering Bernoulli's equation to find velocity,

As there is no loss in energy, Δ Pressure energy ≅ 0

So,

Here 1 and 2 represents top and bottom section of the sprue.

Now substituting for g and 10 in for Δz in velocity equation,

Calculating the area of the basin

Substitute .04 in  for d in the above equation

Calculating the flow rate

Q = 0.1256 x 87.91

Hence the viscosity is and the flow rate is

Calculating the Reynolds number of the flow,

Therefore, the flow is turbulent.

Now considering the solidification time,

Substituting 1.5 for d and 3 for h and 3 min for t to calculate the value of c is

c = 33.33

For case when height is double i.e. h = 6 in

For case when the diameter is doubled i.e. 3 in for d and 3 in  for h,

energy can cross the boundaries of a closed system in the form of heat and mass

explanation: