We are planning to feed 30% HCL acid from totes using gravity. The required flow rate is 10 L/min. Could anyone suggest me the equations used to calculate the height required to achieve this flowrate and the pipe size.
Well first of all you need to specify your destination pressure. You will have to specify your pipe size first - without that you cannot calculate the pipe pressure drop. 10L/min is about 2.6 gpm so your flowrate is tiny - so you do not need a very big pipe.
I did a rough calculation using some assumed numbers. 6ft height totes raised to 10ft above ground level, 3/4" pipe size. The pressure drop comes out to be around 33 kPa. Is there any equation to calculate the flow rate from a outlet pressure/pressure drop thru the system?
I guess I am spoiled as I haven't had to use any equations since university. I am lucky in that I have software to do my hydraulic calculations. I plug in my flowrate, pipe size and schedule and destination pressure and Bob's your uncle!
Why can't you just use a simple Mechanical Energy Balance? Supply P, destination P, pipe diameter, pipe fittings, and elevation should be all you need to calculate flow. Isn't this a basic fluids problem?
The previous posters have left out the equation for flow through a nozzle. They have just allowed for headloss through the discharge pipe.
The equations can be found in Cranes Technical Paper No. 410:
The flow rate from such a tote will not remain constant; it varies as the square root of the height of the remaining acid in the tote. So although the flowrate starts out at a one flow rate, the flowrate steadily decreases as the tote drains.
The velocity of acid exiting the tote is given by SQRT(2gh) where g is acceleration and h is the height of the acid.
So the discharge through the orifice is given byP:
Not sure why you are trying to feed acid by gravity. Unless your application involves feeding acid out of a tote with a constant level, such a gravity feed system will not maintain a constant flow for reasons which should be obvious.
Secondly, if you did figure out a way to get constant flow, you have no easy method to adjust the flow.
Suggest that you install a small postive displacement pump. With a small pump, you can control the feed precisely.
bimr is 100% correct; the flow decreases as the liquid level in the tote drops.
One method is to put a control valve on the line & find the settings for the various liquid liquid levels; maybe wide open when liquid at lowest (bottom of tote). This method is used with 'drip feed' systems for very slow additions of additives to metal plating solutions. A visual flow meter is placed in-line to help if manually controlling the valve.
I agree with the recommendation for a small metering pump to avoid the falling static head (or implement some kind of level control if feasible to maintain static head).
The MEB approach to solve Q for the system described is an interative approach. The MEB can be simplified into the final flow velocity (at the bottom of the pipe) as a function of the friction factor.
1. Choose a friction factor (e.g. 0.0026)
2. Calculate Velocity
3. Calculate Reynolds Number
4. Use Moody Chart to get new friction factor (different than your initial guess unless you're lucky)
5. Calculate new Velocity, Reynolds Number, friction factor
6. Repeat until friction factor converges
7. Take Velocity (from converged friction factor) and convert to Q using cross-sectional area of pipe