Question

A pure magnesium alloy is emptied in a sand mold. If the longitude of the sprue is 1.5 in and 0.5 in diameter. Which is the velocity and the volumetric flux of the metal in the mold? Assume no friction losses and constant pressure durging the process. Is the flux turbulent or laminar? How long will take to fill a casting of 10 in3?

Density of magnesium = 1.65 g/cm3

viscosity = 0.00132 Pa*second

Answer 1

Given :

Length of sprue, h = 1.5 in = 3.81 cm

Diameter of sprue, d = 0.5 in = 1.27 cm

Cross sectional area of sprue, A_{​​​​​​s} = = 1.2667 cm^2

Volume of casting = 10 in^3 = 163.87 cm^3

Density of magnesium = 1.65 g/cm^3

Viscosity of magnesium = 0.00132 Pa*second

Solution :

In the question it is given to assume that there is no friction losses and pressure is constant during the process.

Applying Bernoulli principle, we get velocity at entrance of mould, V_{​​​​m}

V_{​​​​​​m} = √(2gh)

V_{​​​​​​m} = √(2* 981*3.81) = 86.45 cm/s

Volumetric flux, Q = V_{​​​​​​m} * A_{​​​​​​s} = 86.45 * 1.2667 = 109.51 cm^3 /s

To find out if the flux is laminar or turbulent, we will find out the Reynolds number

Re = = 1.65 * 86.45 * 1.27 * 0.1/ .00132 = 13723.93

Considering it as flow through pipe, Reynolds number comes out to be greater than 2000. This implies that the flow is turbulent.

Time taken to fill the casting = Volume of casting / Q

= 163.87 / 109. 51 = 1.496 seconds