# Simple Vertical Gating for Top Gate Time Calculation

In this blog we will learn how to calculate time taken to fill the mold in vertical gating system / top gate moulding .This is very important topic from the competitive exam and casting point of view.Lets try to understand how to calculate the time required to fill the mold in simple vertical gating system.

Assumption

- The flow is steady means (velocity , pressure ,density is not changing with time).
- Mass flow is constant.
- It satisfies all the conditions of Bernoulli's theorem assumption.
- Pressure at point 1 and 3 are equal
- velocity at point 1 is 0. (look diagram for reference)

Let pressure of the fluid is denoted by p

Let velocity of the fluid is denoted by v

Let density of the fluid is denoted by`\rho `

Let gravity is denoted by g

Let the height of the sprue is ` h_{2} `

Let height of the molten metal above the sprue is ` h_{1} `

Let total height of the sprue is ` h_{t} = h_{1}+h_{2}`

Let area of the mold is A

Let height of the mold is H

Derivation

Let apply Bernoullis theorem at point 1 and 3

`\frac{ p_{1} }{ \rho g} +\frac{ v_{1}^{2} }{ 2 g}+ h_{t} =\frac{ p_{3} }{ \rho g} +\frac{ v_{3}^{2} }{ 2 g}+0`

As we said earlier in assumption p1 = p3 and v1 =0

so `v_{3} = \sqrt{2g h_{t} } `

Let `A_{g} ` be the area of cross section at point 3 and v3 be called called as `v_{g} `

If A and H are cross-sectional area of the mold and height of the mold cavity respectively

`A_{g}v_{g}t_{f} = AH `

So the time required to fill the mold cavity is

`t_{f} = \frac{AH }{ A_{g} \sqrt{2g h_{t} } } `

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