Where is the evaporator drain on my 1997 S-10?

The drain pan is under the evaporator. The noise you can hear is air in your coolant system trying to get through the heater matrix. Water doesn't slosh when you are stationary and just started the car.

https://www.fixya.com/cars/r29872074-vehicle_cooling_system_no_heat

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At the bottom of the heater box on the passenger side of the console. Find the rubber drain tube coming off of the heater box

Question I have after reading what you posted is : Left hand or right hand drive? On ones where the evaporator is located on the right (passenger side) there is a short stub hose that protrudes from the engine side of the firewall, even with the bottom of the heater box. That is the evaporator drain.
If the steering is on the right side, I'd imagine the drain would be exactly in the same place only opposite. To avoid confusion, left and right are determined when you are seated inside, not standing in front facing the vehicle.
One note: If you decide to drill into the box, remember that there are components inside. Therefore, drilling needs to be done with a very short bit, only extending from the drill chuck no more than 1/4", or collared so it cannot penetrate further than that..

What kind of car is this? this may be a normal problem. Check your coolant level

Hello Ray.
There could be two things causing this.
First, and most likely, is a plugged drain for the heater evaporator case.
If this drain is plugged, water can accumulate in the box and slosh around.
In the engine compartment, on the firewall, usually on the passenger side, near the bottom there is a small tube sticking out. Run a pipe cleaner or a small wire up inside it and work it around until the debris is cleared.
Secondly, your cooling system may be low on coolant. Air mixed in with the coolant circulates through the heater core creating noise. Check your coolant levels. If it's low, then you should check for leaks in the system.
Thank you for using FixYa.

KL

Drain tube will be attached to the bottom of the heater housing under the hood on firewall.

How do you open the condesate drain on an 05 Impala

Sounds like the sloshing noise is water in the a/c-heater box. The drain is probably plugged. I don't think the sloshing noise is causing the ragged running problem.

dont think it is the heater core making this noise sounds like the drain tube on the evaporator/heater core box is clogged not letting the condensation drain out climb under vehicle find the tube on the passenger side get a can of compressed air spray in tube and see if the water comes out.

It sounds like you may have a blocked drain in the evaporator box. This is where the heater core and evaporator are located.

If you look under the vehicle about where the heater is located, you should see a small tube sticking down ( plastic or rubber ) this should be he drain.

You can squeese the tube open and see if it will drain, If not it may be clogged up with dirt and debris that may require the box to be removed and cleaned.

Check the air inlet, usually located in front of the windsheild, just under the wipers for debris. Keep this area clear. If it has a lot of leaves or other things around it, it can cause water to build up and flood the evaporator box, as well as get down inside.

You may need to take this to a shop that can put it on a lift and get at the drain from the underside, they may be able to clear it without too much troble