Fluid Mechanics - Venturimeter

[partech]

Homework Statement

A horizontal venturimeter is used to measure the flow rate of an oil having density 940kgm-3 in a 16cm diameter pipe. The throat diameter of the venturimeter is 8cm with a discharge coefficient of 0.96. The pressure at inlet is 70kPa and it is required that the pressure at any point should not drop below 55kPa absolute. Find the maximum flow rate for which the meter may be used.

What happens if an oil having a density less than 940kgm-3 flows instead?
Take atmospheric pressure as 1.01 bar.

ρ = 940 Kgm-3
A1 = (π〖(16×〖10〗^(-2))〗^2)/4= 0.0201m²
A2 = (π〖(8×〖10〗^(-2))〗^2)/4= 5.0265×10^-3 m²
Cd = 0.96
P1 = 70KPa (Gauge) = 171KPa (Abs)
P2 = 55KPa (Abs) = -46KPa (Gauge)
ΔP = 116KPa
Q = ?? Find Maximum.

The Attempt at a Solution

For attempt and equation please see attachment 1.

Please if anyone could look over this and give me an idea if it is correct or where i have gone wrong it would be most grateful.

If the fluid was less than the flow would be greater is this correct?

Many Thanks

 

[anathema]

I would like to offer my input on your attempt at solving this problem.

Firstly, your calculations and equations seem to be correct. However, I would like to suggest a few improvements to make your solution more accurate and clear.

1. In your attempt, you have used the atmospheric pressure as 1.01 bar. However, since the problem states that the pressure at inlet is 70kPa, it would be more accurate to use this value as the reference pressure instead of the atmospheric pressure. This would give you a more precise value for the maximum flow rate.

2. In your equation for Q, you have used the absolute pressures for P1 and P2. However, the pressure difference (ΔP) should be calculated using gauge pressures, as the problem states that the pressure at inlet is 70kPa gauge. So the correct equation for Q would be: Q = (Cd * A1 * √(2 * ΔPg))/ρ, where ΔPg is the gauge pressure difference (116kPa in this case).

3. As for the second part of the question, if the oil has a density less than 940kgm-3, then the maximum flow rate would be greater. This is because the venturimeter is designed to measure the flow rate of fluids with a specific density (in this case, 940kgm-3). If the density is less, then the flow rate would be higher for the same pressure difference and discharge coefficient.

I hope this helps clarify any doubts you may have had. Keep up the good work!