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The height of the down sprue is 175 mm and its CS are at the base is 200 mm2. The CS area of the horizontal runner is also 200 mm2.Assuming no losses, indicate the correct choice for-the time (second) required to fill a mould cavity of volume 106mm3. (Use g = 10 m/s2)
[PI 2002]
  • a)
    2.67
  • b)
    8.45
  • c)
    26.7
  • d)
    84.50
Correct answer is option 'A'. Can you explain this answer?
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To solve this problem, we can use the formula for volumetric flow rate:

Q = A * v

Where:
Q = volumetric flow rate (mm^3/s)
A = cross-sectional area (mm^2)
v = velocity (mm/s)

We are given the cross-sectional area of the down sprue and the horizontal runner, both of which are 200 mm^2. Therefore, the cross-sectional area for the flow of molten metal into the mould cavity is also 200 mm^2.

Now let's find the velocity of the molten metal. We can use the equation for the volume of a cylinder:

V = A * h

Where:
V = volume (mm^3)
A = cross-sectional area (mm^2)
h = height (mm)

We are given the volume of the mould cavity, which is 106 mm^3. The height of the down sprue is 175 mm. Therefore, we can rearrange the equation to solve for the cross-sectional area of the mould cavity:

A = V / h
A = 106 mm^3 / 175 mm
A = 0.6057 mm^2

Now we can substitute the values into the volumetric flow rate equation:

Q = 0.6057 mm^2 * v

Since the cross-sectional area of the mould cavity is the same as the down sprue and the horizontal runner, the volumetric flow rate is the same for all three sections.

Now we need to find the time required to fill the mould cavity. We can rearrange the equation to solve for time:

t = V / Q
t = 106 mm^3 / (0.6057 mm^2 * v)

Finally, we can substitute the given acceleration due to gravity, g, to find the time in seconds:

t = 106 mm^3 / (0.6057 mm^2 * v * 10 m/s^2)
t = 2.67 s

Therefore, the correct choice is option A, 2.67 seconds.
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The height of the down sprue is 175 mm and its CS are at the base is 200 mm2. The CS area of the horizontal runner is also 200 mm2.Assuming no losses, indicate the correct choice for-the time (second) required to fill a mould cavity of volume 106mm3. (Use g = 10 m/s2)[PI 2002]a)2.67b)8.45c)26.7d)84.50Correct answer is option 'A'. Can you explain this answer?
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