# Bernoulli Equation Problem

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Q) In a production line fluid C is produced. When the bottle comes under the filling heads, fluid A and fluid B are poured into it from separate tanks through two separate tubes.

The final product contains fluid A and fluid B are in a ratio of 1:4 by volume.

Once the bottle is underneath the filling heads, both liquids are filled in exactly the same time so that the bottle can move down the line for sealing and capping and another bottle can be filled up.

a) If the diameter of the fluid A tube is double that of the fluid B

tube, what is the ratio of the velocity of the fluid A: fluid B in their tubes?

b) What is the ratio of the mass flow rate of fluid A: fluid B in their tubes?

heres my working and i think i got the first part right but not sure how to do the second part.

https://pasteboard.co/JBtLiSI.jpg

The final product contains fluid A and fluid B are in a ratio of 1:4 by volume.

Once the bottle is underneath the filling heads, both liquids are filled in exactly the same time so that the bottle can move down the line for sealing and capping and another bottle can be filled up.

a) If the diameter of the fluid A tube is double that of the fluid B

tube, what is the ratio of the velocity of the fluid A: fluid B in their tubes?

b) What is the ratio of the mass flow rate of fluid A: fluid B in their tubes?

heres my working and i think i got the first part right but not sure how to do the second part.

https://pasteboard.co/JBtLiSI.jpg

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#2

(Original post by

Q) In a production line fluid C is produced. When the bottle comes under the filling heads, fluid A and fluid B are poured into it from separate tanks through two separate tubes.

The final product contains fluid A and fluid B are in a ratio of 1:4 by volume.

Once the bottle is underneath the filling heads, both liquids are filled in exactly the same time so that the bottle can move down the line for sealing and capping and another bottle can be filled up.

a) If the diameter of the fluid A tube is double that of the fluid B

tube, what is the ratio of the velocity of the fluid A: fluid B in their tubes?

b) What is the ratio of the mass flow rate of fluid A: fluid B in their tubes?

heres my working and i think i got the first part right but not sure how to do the second part.

https://pasteboard.co/JBtLiSI.jpg

**aoifaosf24**)Q) In a production line fluid C is produced. When the bottle comes under the filling heads, fluid A and fluid B are poured into it from separate tanks through two separate tubes.

The final product contains fluid A and fluid B are in a ratio of 1:4 by volume.

Once the bottle is underneath the filling heads, both liquids are filled in exactly the same time so that the bottle can move down the line for sealing and capping and another bottle can be filled up.

a) If the diameter of the fluid A tube is double that of the fluid B

tube, what is the ratio of the velocity of the fluid A: fluid B in their tubes?

b) What is the ratio of the mass flow rate of fluid A: fluid B in their tubes?

heres my working and i think i got the first part right but not sure how to do the second part.

https://pasteboard.co/JBtLiSI.jpg

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#4

(Original post by

I am slightly confused then, so what is the ratio of the velocities?

**aoifaosf24**)I am slightly confused then, so what is the ratio of the velocities?

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#5

(Original post by

I am slightly confused then, so what is the ratio of the velocities?

**aoifaosf24**)I am slightly confused then, so what is the ratio of the velocities?

Where:

X = Use velocity from volumetric flow rate in pipe A

Y = Use velocity from volumetric flow rate in pipe B

Last edited by 0le; 2 months ago

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(Original post by

What are you confused with?

**Eimmanuel**)What are you confused with?

I understand Ab=pi*(Db/2)^2 but if Da=2Db then Db=Da/2 so shouldn't Ab=pi*[(Da/2)/2]^2 => Ab=pi*(Da/4)^2 => Ab=(pi*Da^2)/16

And then as Aa=(pi*Da^2)/4 we can equate the two and get the equation 4Aa=16Ab and therefore Aa=4Ab.

So im just confused with how you got 4Aa=Ab

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#7

(Original post by

Im confused with how you got the second line.

I understand Ab=pi*(Db/2)^2 but if Da=2Db then Db=Da/2 so shouldn't Ab=pi*[(Da/2)/2]^2 => Ab=pi*(Da/4)^2 => Ab=(pi*Da^2)/16

And then as Aa=(pi*Da^2)/4 we can equate the two and get the equation 4Aa=16Ab and therefore Aa=4Ab.

So im just confused with how you got 4Aa=Ab

**aoifaosf24**)Im confused with how you got the second line.

I understand Ab=pi*(Db/2)^2 but if Da=2Db then Db=Da/2 so shouldn't Ab=pi*[(Da/2)/2]^2 => Ab=pi*(Da/4)^2 => Ab=(pi*Da^2)/16

And then as Aa=(pi*Da^2)/4 we can equate the two and get the equation 4Aa=16Ab and therefore Aa=4Ab.

So im just confused with how you got 4Aa=Ab

It is supposed to be as edited below.

4

*Q*

_{A}=

*u*

_{A}

*A*

_{A}

*Q*

_{B}=

*u*

_{B}(4

*A*

_{B})

which (IMO) do not make sense.

Last edited by Eimmanuel; 2 months ago

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(Original post by

You are right that I make a mistake.

It is supposed to be as edited below.

I was puzzled by your statement in the working:

4

which (IMO) do not make sense.

**Eimmanuel**)You are right that I make a mistake.

It is supposed to be as edited below.

I was puzzled by your statement in the working:

4

*Q*_{A}=*u*_{A}*A*_{A}*Q*_{B}=*u*_{B}(4*A*_{B})which (IMO) do not make sense.

So now i have the equations Qb=Ub(Aa/4) and Qa=UaAa and as 4Qa=Qb [because of the 1:4 (A:B) ratio in the bottle]

So Qb/4=UaAa and Qb=Ub(Aa/4) and therefore Ua=Qb/4Aa and Ub=4Qb/Aa => Ua/Ub=(Qb/4a)/4Qb/Aa) => Ua/Ub=QbAa/16QbAa => Ua/Ub=1/16

so i can conclude Ua : Ub = 1:16

Last edited by aoifaosf24; 2 months ago

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#9

(Original post by

Sorry about that.

So now i have the equations Qb=Ub(Aa/4) and Qa=UaAa and as 4Qa=Qb [because of the 1:4 (A:B) ratio in the bottle]

So Qb/4=UaAa and Qb=Ub(Aa/4) and therefore Ua=Qb/4Aa and Ub=4Qb/Aa => Ua/Ub=(Qb/4a)/4Qb/Aa) => Ua/Ub=QbAa/16QbAa => Ua/Ub=1/16

so i can conclude Ua : Ub = 1:16

**aoifaosf24**)Sorry about that.

So now i have the equations Qb=Ub(Aa/4) and Qa=UaAa and as 4Qa=Qb [because of the 1:4 (A:B) ratio in the bottle]

So Qb/4=UaAa and Qb=Ub(Aa/4) and therefore Ua=Qb/4Aa and Ub=4Qb/Aa => Ua/Ub=(Qb/4a)/4Qb/Aa) => Ua/Ub=QbAa/16QbAa => Ua/Ub=1/16

so i can conclude Ua : Ub = 1:16

Your working seems good.

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