Answer:
(a) Velocity at bottom is 1.85 m/s
(b) Volume flow rate is 7.4 x 10⁻⁴ m³/s.
(c) The time required to fill the mold is 1.35 s.
Explanation:
(a)
Applying Bernoulli's Equation on both ends of the down sprue, with the assumptions that every point is at atmospheric pressure and the liquid metal at the pouring basin is at zero velocity. The equation then becomes:
V = √2gh
where,
V = velocity at bottom of down sprue
h = height of down sprue = 175 mm = 0.175 m
V = √2(9.8 m/s²)(0.175 m)
V = 1.85 m/s
(b)
The volume flow rate is given as:
Volume Flow Rate = (V)(A)
where,
V = velocity at bottom = 1.85 m/s
A = Area of bottom = 400 mm² = 0.0004 m²
Therefore,
Volume Flow Rate = (1.85 m/s)(0.0004 m²)
Volume Flow Rate = 7.4 x 10⁻⁴ m³/s = 740 cm³/s
(c)
The time required to fill the cavity is given as:
Volume Flow Rate = V/t
where,
V = Volume of mold Cavity = 0.001 m³
t = time required to fill the cavity = ?
Therefore,
t = V/Volume Flow Rate
t = 0.001 m³/7.4 x 10⁻⁴ m³/s
t = 1.35 s
