The cowl is a grille by the windshield, used on most cars since fresh air heating and ventilation became common. Automakers put in drains for the water that gets in, but, until the 1990s, did little to keep leaves, twigs, and other debris from blocking those rather small drains. Most cars will clog their cowl drains from time to time, if driven or left outside in the fall.
Cleaning in the Volaré engine compartment, I nudged a piece of rubber fitted against the firewall [the cowl drain] and out came a flow of water. ... by poking my finger around in the space I dislodged a bunch of leaves and sludge. There are two other similar pieces of rubber on the firewall, three altogether; two towards the sides and one in the middle. I saw some serious corrosion under the opening in the middle of the firewall. I scraped it with an abrasive pad and applied some anti-rust primer, but there's probably more rust in the area of the middle drain that I can’t see. matte black drain
Common locations for the drains are behind the windshield wiper motor, and between the fender and the firewall, one on each side of the car. There is usually another drain for the vent fan.
Many cars had cowl drain flaps to cover the drains and prevent detritus from entering; these can get stuck in place or seal themselves shut, but the aftemarket sells them for under $10. Owners of 1975-76 Valiants (and possibly other cars) can likely get a 1974 unit (many parts sellers only verify A-body fit up to 1974).
Valiants and related cars (Darts, Dusters, etc) often leaked through the windshield wiper pivots. On the 1968-1976 cars, it tends to go straight into the dashboard (and you can see the pivot holes if you lower the wiper assembly, so this is by design). Replacing the pivot seals should fix it, if you use the proper sealing and are lucky. This is not an easy job if you have air conditioning.
Phil Gatto added, “When it rained, gallons of water would literally pour on to the front passenger floorboards [of my 1971 Dodge Charger]. I traced it to that rubber flap; it was totally clogged with dirt from crushed leaves. After cleaning it out all was well. I had the same problem with my 2011 Dodge Avenger, but there was no flap that I could find and so I took it to the dealer; they said that car has two drains and both were clogged. They are much harder to get to on the Avenger, though easy for someone with a lift. They cleaned them out and I haven’t had any trouble since.”
On the 1970s Valiant/Dart, there is an additional drain for the air conditioner condensate which also clogs, which starts at back of the “big black box” on the passenger side (covering the evaporator), makes a 90° turn out in the open, and goes through the firewall. Over time this too can clog.
kitchen sink pipes Gary Platz added: “When I bought our 1980 Cordoba, I removed the plastic grills and both vacuumed and blew out debris with compressed air. Then, I sprayed rust proofing in those areas. I once owned a 1979 Volare that had a lot of tree debris in the cowling, to the point of rot on the passenger side, as the car was parked under a tree every day. I tried to repair the hole but, due to its location, it was impossible. I pulled the floor body plug and rust proofed the floor and put a plastic grid under the carpet so the water could escape; it kept the floor from rotting for fourteen years. I did the same on the Duster, Cordoba, and Rampage as a precautionary measure.”