In a sand casting process, a sprue of 10 mm base diameter and 200 mm height leads to a runner which fills a cubical cavity of 100 mm side. What will be the volume flow rate of metal? [Acceleration due to gravity = 10 m/s², π = 3.14]

Concept:

The volume flow rate of metal in a sand casting process can be determined using Torricelli’s theorem, which states that the velocity of fluid flow under gravity is:

\( v = \sqrt{2gh} \)

The volume flow rate Q is given by:

\( Q = A v \)

where:

• A = Cross-sectional area of the sprue
• v = Velocity of the molten metal

Given:

• Diameter of sprue base: d = 10 mm
• Height of sprue: h = 200 mm
• Acceleration due to gravity: g = 10 m/s²
• π = 3.14

Calculation:

Step 1: Compute velocity using Torricelli’s theorem

\( v = \sqrt{2gh} = \sqrt{2 \times 10 \times 0.2} \)

\( v = \sqrt{4} = 2~m/s\)

Step 2: Compute cross-sectional area of the sprue

\( A = \frac{π d^2}{4} = \frac{3.14 \times (10 \times 10^{-3})^2}{4} \)

\( A = \frac{3.14 \times 100 \times 10^{-6}}{4} = 7.85 \times 10^{-6}~m^2\)

Step 3: Compute volume flow rate

\( Q = A v = (7.85 \times 10^{-6}) \times 2 \)

\( Q = 15.7 \times 10^{-6}~m^3 /s\)

Converting to mm³/s:

\( Q = 15700~mm^3 /s\)