Fluids Mixing at Two Different Pressures

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A lot will depend on the shape of the mixing point and the point of measurement.

If configured as a venturi,the larger flow will actually suck the smaller flow into the main larger flow stream.

The length and diameter of the pipe after the mixing point is also an important factor.

Lots of variables to consider.

More info=More feedback.

I am not able to attach the picture. It is basically two streams of chemicals mixed and going into a tank.

The first positive displacement pump 1 pumps 6 BPM through a 4" pipe. The second displacement pump 2 pumps 0.8 BPM through a 1" pipe. They meet at a point and the discharge to the tank is also 4". The 1 inch line is joined to the 4" line via a couple of expansion joints. I hope this is clear.

I still need to know the pressure at Pm to ensure that from that point to the tank, I have enough pressure to overcome the back pressure of the piping between the Pm to the tank. How will i be able to determine the pressure at Pm?

You specified the flow rate at each pump. To deliver that flow rate, the pump has to produce a pressure that maintains that flow rate against the flow resistance of the pipes.

You can't specify both the flow rate and pressure at the pump. If you specify flow rate, you can calculate pressure using the flow resistance of the pipes. If you specify pressure, you can calculate flow rate using the flow resistance of the pipes.

It's like an electrical circuit. If you put a resistor of resistance R across a battery of voltage V, you can calculate current I = V / R. If you know the current I, you can calculate voltage V = I x R.

If you have "positive displacement pumps" (like piston or screw pumps), they supply a nominal constant flow regardless of the pressure, until their max operating pressure or motor power limit. According to this, pressure at Pm is only due to the pressure drop of the pipe Pm to Tank. The pressure at P1 and P2 is the sum of the pressure at Pm plus respectively the pressure drop of the pipe P1 to Pm and P2 to Pm. To calculate these pressures you can use the equation posted above by Rixter. The difficulty of that equation is the compute of "Friction Factor". I can help you a little on this factor as below:

1. first calculate the Reynolds Number Re = W*D/v where

W is the fluid velocity in "m/s"

D is the pipe internal diameter in "m"

v is the Fluid Kinematic Viscosity in "cSt"

2. secondly calculate the Friction Factor acc.to the following:

IF Re < 2300 then 64/Re

IF Re >= 2300 then 0.25*LOG10((k/(3,7*D))+(5,74/Re^0,9))^(-2))

where k is the Absolute Roughness of the pipe in "mm"

To be more precise, the equation posted by Rixter should be completed by adding to L/D the ∑Le/D , where each Le/D represents the Equivalent Length of the fittings in the piping route, like valves, elbows, bends, joints and tees.

(L/D+∑L_e/D)

https://www.advancedconverter.com/unit-conversions/flow-conversion/barrels-per-minute-to-gallons-per-minute

http://irrigation.wsu.edu/Content/Calculators/General/Pipe-Velocity.php

The pressure at the mixing point is only related to the pressure drop due to the flow of 6.8 <...BPM...> downstream, assuming no chemical reaction, and whatever discharge arrangements are provided where the fluid enters the tank. There are established formulae for pressure drop in pipes that go back to Osborne Reynolds’ initial experiments in 1875.

Most Process Engineers wouldn’t need to calculate it. If it is a relevant process measurement then a pressure gauge installed at the mixing point would be a worthwhile addition to the equipment already provided.

if there were a risk of blockage as a result of reaction of the two fluids then some way of protecting the arrangements from over-pressure would be provided.

What was the outcome of the HazOp Study for this plant?

Let's say the discharge pressure of fluid 1 is 120 psi and the discharge at fluid 2 is about 30 psi. Will there be an issue of the fluid pumped from P2, since the discharge pressure of P2 is small compared to dicharge pressure at P1? Will there be a proper mix?

The concept of two different discharge pressures is invalid, Mildred.

With your pipe size & flow, it is unlikely you can have both flow and pressure as you describe at each pump discharge, but it is theoretically possible. The pressures indicate a very long 4” pipe length, a very high discharge elevation or an extremely viscous liquid.

<...Let's say...> that's nonsense.

As I stated,it depends on the shape of the mixing point.Is it a "Y" shape or a straight "Tee" shape?

If the larger flow is at a velocity higher than the lower flow,(determined by pipe size) and the lower flow is joined at the proper angle to the larger flow,there will be a venturi effect that will present a negative pressure to the smaller flow.

If the mixing point is designed to actually mix the two flows,this is probably the way it is designed.

Since both pumps are PD pumps,it will not matter what the back pressure is,they will pump the same volume of fluid,up to the limits of the pumps.

If you must know and are tasked to specify a pressure measurement device for the junction,a Bordon-tube gauge is the simplest and cheapest way to go.

Digital versions are available,but more expensive,

The two fluids will not mix but just flow in two slightly intermingled streams along the discharge pipe into the tank. The pressure at the junction point will be determined by the back pressure created by the discharge pipe for the combined flow rate. In order to get any mixing you need to add a "static mixer" into the discharge pipe. They are not expensive, have no moving parts, consume a tiny amount of power (a marginal increase to pump amperage), require little or no maintenance, last 'forever', don't add much to the pressure drop and give very consistent results. When specifying one you need to know the "Coefficient of Variation" COV. which is a measure of how well you want the fluids mixed. Check out the SULZER web site for a good description of how they work. There are lots of manufacturers. Choose one near you with facilities to demonstrate how their mixers perform with your ingredients and flow rates.

https://en.wikipedia.org/wiki/Static_mixer