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## Homework Statement

Determine the flow rate, Q.

Ignore energy losses.

Given:

D

_{1}= 100 mm

D

_{2}= 75 mm

Fluid in the pipe is water.

Fluid in the metre is mercury.

S.G. of Mercury is ~13.6.

The difference in height of the mecury columns is 80mm.

Diagram is below.

## Homework Equations

Bernoulli's Equation.

Equation of Continuity. (Q

_{1}= Q

_{2})

## The Attempt at a Solution

I approached this as a manometer question, but with that orifice in the flow I was unsure on how to proceed. I chose a datum as the lower of the two levels of mercury. The expressions I got were:

P

_{x-x}= Pressure due to the flow + Pressure due to the height of the water above the mercury + the pressure due to the mercury above the datum. This was for the left hand side.

P

_{x-x}= P

_{1}+ ρ

_{w}gh + ρ

_{m}gh', where h' = 80 mm and h is an unknown height which cancels out when the left side and right side are equated.

For the right hand side I said

P

_{x-x}= Pressure due to the flow + Pressure due to the height of the water.

P

_{x-x}= P

_{2}+ ρ

_{w}g(h+h')

For this second equation I feel there is something missing, surely that opening in the flow causes an additional term to be added?