diff --git a/pydantic/networks.py b/pydantic/networks.py
--- a/pydantic/networks.py
+++ b/pydantic/networks.py
@@ -298,7 +298,16 @@ class HttpUrl(AnyUrl):
 
 
 class PostgresDsn(AnyUrl):
-    allowed_schemes = {'postgres', 'postgresql'}
+    allowed_schemes = {
+        'postgres',
+        'postgresql',
+        'postgresql+asyncpg',
+        'postgresql+pg8000',
+        'postgresql+psycopg2',
+        'postgresql+psycopg2cffi',
+        'postgresql+py-postgresql',
+        'postgresql+pygresql',
+    }
     user_required = True
 
 

diff --git a/tests/test_networks.py b/tests/test_networks.py
--- a/tests/test_networks.py
+++ b/tests/test_networks.py
@@ -18,7 +18,12 @@
         'https://example.org/whatever/next/',
         'postgres://user:pass@localhost:5432/app',
         'postgres://just-user@localhost:5432/app',
+        'postgresql+asyncpg://user:pass@localhost:5432/app',
+        'postgresql+pg8000://user:pass@localhost:5432/app',
         'postgresql+psycopg2://postgres:postgres@localhost:5432/hatch',
+        'postgresql+psycopg2cffi://user:pass@localhost:5432/app',
+        'postgresql+py-postgresql://user:pass@localhost:5432/app',
+        'postgresql+pygresql://user:pass@localhost:5432/app',
         'foo-bar://example.org',
         'foo.bar://example.org',
         'foo0bar://example.org',
@@ -333,6 +338,10 @@ class Model(BaseModel):
 
     assert Model(a='postgres://user:pass@localhost:5432/app').a == 'postgres://user:pass@localhost:5432/app'
     assert Model(a='postgresql://user:pass@localhost:5432/app').a == 'postgresql://user:pass@localhost:5432/app'
+    assert (
+        Model(a='postgresql+asyncpg://user:pass@localhost:5432/app').a
+        == 'postgresql+asyncpg://user:pass@localhost:5432/app'
+    )
 
     with pytest.raises(ValidationError) as exc_info:
         Model(a='http://example.org')

Can't use `postgresql+psycopg2://...` with `PostgresDsn `
### Checks

* [x] I added a descriptive title to this issue
* [x] I have searched (google, github) for similar issues and couldn't find anything
* [x] I have read and followed [the docs](https://pydantic-docs.helpmanual.io/) and still think this is a bug

<!-- Sorry to sound so draconian, but every second saved replying to issues is time spend improving pydantic :-) -->

# Bug

I'm expecting to be able to use a database connection url such as `postgresql+psycopg2://user:pass@localhost:5432/app` (a format [SQLAlchemy is supporting](https://docs.sqlalchemy.org/en/14/dialects/postgresql.html#dialect-postgresql-psycopg2-connect)). 

However, it doesn't seem to accept the `+psycopg2` part. 

Output of `python -c "import pydantic.utils; print(pydantic.utils.version_info())"`:
```
             pydantic version: 1.8.1
            pydantic compiled: False
                 install path: /Users/krisb/Code/fork/pydantic/pydantic
               python version: 3.7.10 (default, Apr 12 2021, 03:46:49)  [Clang 12.0.0 (clang-1200.0.32.29)]
                     platform: Darwin-20.3.0-x86_64-i386-64bit
     optional deps. installed: ['devtools', 'dotenv', 'email-validator', 'typing-extensions']
```
<!-- or if you're using pydantic prior to v1.3, manually include: OS, python version and pydantic version -->

<!-- Please read the [docs](https://pydantic-docs.helpmanual.io/) and search through issues to
confirm your bug hasn't already been reported. -->

<!-- Where possible please include a self-contained code snippet describing your bug: -->

Changed test https://github.com/samuelcolvin/pydantic/blob/7af90a8d6c1c406799ad95b81e353b386cde5745/tests/test_networks.py#L318-L318 to include 
```py
assert Model(a='postgresql+psycopg2://user:pass@localhost:5432/app').a == 'postgresql+psycopg2://user:pass@localhost:5432/app'
```
pytest error output:
```
...
>           raise validation_error
E           pydantic.error_wrappers.ValidationError: 1 validation error for Model
E           a
E             URL scheme not permitted (type=value_error.url.scheme; allowed_schemes={'postgres', 'postgresql'})

pydantic/main.py:400: ValidationError
```

This is similar to https://github.com/samuelcolvin/pydantic/issues/1142, and a workaround for now is to use `AnyUrl` where this type of URL is supported. 


tests/test_networks.py::test_postgres_dsns
tests/test_networks.py::test_any_url_success[http://example.org] tests/test_networks.py::test_any_url_success[http://test] tests/test_networks.py::test_any_url_success[http://localhost0] tests/test_networks.py::test_any_url_success[https://example.org/whatever/next/] tests/test_networks.py::test_any_url_success[postgres://user:pass@localhost:5432/app] tests/test_networks.py::test_any_url_success[postgres://just-user@localhost:5432/app] tests/test_networks.py::test_any_url_success[postgresql+asyncpg://user:pass@localhost:5432/app] tests/test_networks.py::test_any_url_success[postgresql+pg8000://user:pass@localhost:5432/app] tests/test_networks.py::test_any_url_success[postgresql+psycopg2://postgres:postgres@localhost:5432/hatch] tests/test_networks.py::test_any_url_success[postgresql+psycopg2cffi://user:pass@localhost:5432/app] tests/test_networks.py::test_any_url_success[postgresql+py-postgresql://user:pass@localhost:5432/app] tests/test_networks.py::test_any_url_success[postgresql+pygresql://user:pass@localhost:5432/app] tests/test_networks.py::test_any_url_success[foo-bar://example.org] tests/test_networks.py::test_any_url_success[foo.bar://example.org] tests/test_networks.py::test_any_url_success[foo0bar://example.org] tests/test_networks.py::test_any_url_success[https://example.org] tests/test_networks.py::test_any_url_success[http://localhost1] tests/test_networks.py::test_any_url_success[http://localhost/] tests/test_networks.py::test_any_url_success[http://localhost:8000] tests/test_networks.py::test_any_url_success[http://localhost:8000/] tests/test_networks.py::test_any_url_success[https://foo_bar.example.com/] tests/test_networks.py::test_any_url_success[ftp://example.org] tests/test_networks.py::test_any_url_success[ftps://example.org] tests/test_networks.py::test_any_url_success[http://example.co.jp] tests/test_networks.py::test_any_url_success[http://www.example.com/a%C2%B1b] tests/test_networks.py::test_any_url_success[http://www.example.com/~username/] tests/test_networks.py::test_any_url_success[http://info.example.com?fred] tests/test_networks.py::test_any_url_success[http://info.example.com/?fred] tests/test_networks.py::test_any_url_success[http://xn--mgbh0fb.xn--kgbechtv/] tests/test_networks.py::test_any_url_success[http://example.com/blue/red%3Fand+green] tests/test_networks.py::test_any_url_success[http://www.example.com/?array%5Bkey%5D=value] tests/test_networks.py::test_any_url_success[http://xn--rsum-bpad.example.org/] tests/test_networks.py::test_any_url_success[http://123.45.67.8/] tests/test_networks.py::test_any_url_success[http://123.45.67.8:8329/] tests/test_networks.py::test_any_url_success[http://[2001:db8::ff00:42]:8329] tests/test_networks.py::test_any_url_success[http://[2001::1]:8329] tests/test_networks.py::test_any_url_success[http://[2001:db8::1]/] tests/test_networks.py::test_any_url_success[http://www.example.com:8000/foo] tests/test_networks.py::test_any_url_success[http://www.cwi.nl:80/%7Eguido/Python.html] tests/test_networks.py::test_any_url_success[https://www.python.org/\u043f\u0443\u0442\u044c] tests/test_networks.py::test_any_url_success[http://\u0430\u043d\u0434\u0440\u0435\u0439@example.com] tests/test_networks.py::test_any_url_success[https://example.com] tests/test_networks.py::test_any_url_success[https://exam_ple.com/] tests/test_networks.py::test_any_url_success[http://twitter.com/@handle/] tests/test_networks.py::test_any_url_success[http://11.11.11.11.example.com/action] tests/test_networks.py::test_any_url_success[http://abc.11.11.11.11.example.com/action] tests/test_networks.py::test_any_url_invalid[http:///example.com/-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[https:///example.com/-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[http://.example.com:8000/foo-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[https://example.org\\-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[https://exampl$e.org-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[http://??-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[http://.-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[http://..-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[https://example.org tests/test_networks.py::test_any_url_invalid[$https://example.org-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[../icons/logo.gif-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[abc-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[..-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[/-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[+http://example.com/-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[ht*tp://example.com/-value_error.url.scheme-invalid tests/test_networks.py::test_any_url_invalid[ tests/test_networks.py::test_any_url_invalid[-value_error.any_str.min_length-ensure tests/test_networks.py::test_any_url_invalid[None-type_error.none.not_allowed-none tests/test_networks.py::test_any_url_invalid[http://2001:db8::ff00:42:8329-value_error.url.extra-URL tests/test_networks.py::test_any_url_invalid[http://[192.168.1.1]:8329-value_error.url.host-URL tests/test_networks.py::test_any_url_invalid[http://example.com:99999-value_error.url.port-URL tests/test_networks.py::test_any_url_parts tests/test_networks.py::test_url_repr tests/test_networks.py::test_ipv4_port tests/test_networks.py::test_ipv4_no_port tests/test_networks.py::test_ipv6_port tests/test_networks.py::test_int_domain tests/test_networks.py::test_co_uk tests/test_networks.py::test_user_no_password tests/test_networks.py::test_user_info_no_user tests/test_networks.py::test_at_in_path tests/test_networks.py::test_fragment_without_query tests/test_networks.py::test_http_url_success[http://example.org] tests/test_networks.py::test_http_url_success[http://example.org/foobar] tests/test_networks.py::test_http_url_success[http://example.org.] tests/test_networks.py::test_http_url_success[http://example.org./foobar] tests/test_networks.py::test_http_url_success[HTTP://EXAMPLE.ORG] tests/test_networks.py::test_http_url_success[https://example.org] tests/test_networks.py::test_http_url_success[https://example.org?a=1&b=2] tests/test_networks.py::test_http_url_success[https://example.org#a=3;b=3] tests/test_networks.py::test_http_url_success[https://foo_bar.example.com/] tests/test_networks.py::test_http_url_success[https://exam_ple.com/] tests/test_networks.py::test_http_url_success[https://example.xn--p1ai] tests/test_networks.py::test_http_url_success[https://example.xn--vermgensberatung-pwb] tests/test_networks.py::test_http_url_success[https://example.xn--zfr164b] tests/test_networks.py::test_http_url_invalid[ftp://example.com/-value_error.url.scheme-URL tests/test_networks.py::test_http_url_invalid[http://foobar/-value_error.url.host-URL tests/test_networks.py::test_http_url_invalid[http://localhost/-value_error.url.host-URL tests/test_networks.py::test_http_url_invalid[https://example.123-value_error.url.host-URL tests/test_networks.py::test_http_url_invalid[https://example.ab123-value_error.url.host-URL tests/test_networks.py::test_http_url_invalid[xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx-value_error.any_str.max_length-ensure tests/test_networks.py::test_coerse_url[ tests/test_networks.py::test_coerse_url[https://www.example.com-https://www.example.com] tests/test_networks.py::test_coerse_url[https://www.\u0430\u0440\u0440\u04cf\u0435.com/-https://www.xn--80ak6aa92e.com/] tests/test_networks.py::test_coerse_url[https://exampl\xa3e.org-https://xn--example-gia.org] tests/test_networks.py::test_coerse_url[https://example.\u73e0\u5b9d-https://example.xn--pbt977c] tests/test_networks.py::test_coerse_url[https://example.verm\xf6gensberatung-https://example.xn--vermgensberatung-pwb] tests/test_networks.py::test_coerse_url[https://example.\u0440\u0444-https://example.xn--p1ai] tests/test_networks.py::test_coerse_url[https://exampl\xa3e.\u73e0\u5b9d-https://xn--example-gia.xn--pbt977c] tests/test_networks.py::test_parses_tld[ tests/test_networks.py::test_parses_tld[https://www.example.com-com] tests/test_networks.py::test_parses_tld[https://www.example.com?param=value-com] tests/test_networks.py::test_parses_tld[https://example.\u73e0\u5b9d-xn--pbt977c] tests/test_networks.py::test_parses_tld[https://exampl\xa3e.\u73e0\u5b9d-xn--pbt977c] tests/test_networks.py::test_parses_tld[https://example.verm\xf6gensberatung-xn--vermgensberatung-pwb] tests/test_networks.py::test_parses_tld[https://example.\u0440\u0444-xn--p1ai] tests/test_networks.py::test_parses_tld[https://example.\u0440\u0444?param=value-xn--p1ai] tests/test_networks.py::test_redis_dsns tests/test_networks.py::test_custom_schemes tests/test_networks.py::test_build_url[kwargs0-ws://foo@example.net] tests/test_networks.py::test_build_url[kwargs1-ws://foo:x@example.net] tests/test_networks.py::test_build_url[kwargs2-ws://example.net?a=b#c=d] tests/test_networks.py::test_build_url[kwargs3-http://example.net:1234] tests/test_networks.py::test_son tests/test_networks.py::test_address_valid[foobar@example.com-foobar-foobar@example.com] tests/test_networks.py::test_address_valid[s@muelcolvin.com-s-s@muelcolvin.com] tests/test_networks.py::test_address_valid[Samuel tests/test_networks.py::test_address_valid[foobar tests/test_networks.py::test_address_valid[ tests/test_networks.py::test_address_valid[foo.bar@example.com tests/test_networks.py::test_address_valid[foo tests/test_networks.py::test_address_valid[FOO tests/test_networks.py::test_address_valid[<FOOBAR@example.com> tests/test_networks.py::test_address_valid[\xf1o\xf1\xf3@example.com-\xf1o\xf1\xf3-\xf1o\xf1\xf3@example.com] tests/test_networks.py::test_address_valid[\u6211\u8cb7@example.com-\u6211\u8cb7-\u6211\u8cb7@example.com] tests/test_networks.py::test_address_valid[\u7532\u6590\u9ed2\u5ddd\u65e5\u672c@example.com-\u7532\u6590\u9ed2\u5ddd\u65e5\u672c-\u7532\u6590\u9ed2\u5ddd\u65e5\u672c@example.com] tests/test_networks.py::test_address_valid[\u0447\u0435\u0431\u0443\u0440\u0430\u0448\u043a\u0430\u044f\u0449\u0438\u043a-\u0441-\u0430\u043f\u0435\u043b\u044c\u0441\u0438\u043d\u0430\u043c\u0438.\u0440\u0444@example.com-\u0447\u0435\u0431\u0443\u0440\u0430\u0448\u043a\u0430\u044f\u0449\u0438\u043a-\u0441-\u0430\u043f\u0435\u043b\u044c\u0441\u0438\u043d\u0430\u043c\u0438.\u0440\u0444-\u0447\u0435\u0431\u0443\u0440\u0430\u0448\u043a\u0430\u044f\u0449\u0438\u043a-\u0441-\u0430\u043f\u0435\u043b\u044c\u0441\u0438\u043d\u0430\u043c\u0438.\u0440\u0444@example.com] tests/test_networks.py::test_address_valid[\u0909\u0926\u093e\u0939\u0930\u0923.\u092a\u0930\u0940\u0915\u094d\u0937@domain.with.idn.tld-\u0909\u0926\u093e\u0939\u0930\u0923.\u092a\u0930\u0940\u0915\u094d\u0937-\u0909\u0926\u093e\u0939\u0930\u0923.\u092a\u0930\u0940\u0915\u094d\u0937@domain.with.idn.tld] tests/test_networks.py::test_address_valid[foo.bar@example.com-foo.bar-foo.bar@example.com] tests/test_networks.py::test_address_valid[foo.bar@exam-ple.com tests/test_networks.py::test_address_valid[\u03b9\u03c9\u03ac\u03bd\u03bd\u03b7\u03c2@\u03b5\u03b5\u03c4\u03c4.gr-\u03b9\u03c9\u03ac\u03bd\u03bd\u03b7\u03c2-\u03b9\u03c9\u03ac\u03bd\u03bd\u03b7\u03c2@\u03b5\u03b5\u03c4\u03c4.gr] tests/test_networks.py::test_address_invalid[f tests/test_networks.py::test_address_invalid[foo.bar@exam\nple.com tests/test_networks.py::test_address_invalid[foobar] tests/test_networks.py::test_address_invalid[foobar tests/test_networks.py::test_address_invalid[@example.com] tests/test_networks.py::test_address_invalid[foobar@.example.com] tests/test_networks.py::test_address_invalid[foobar@.com] tests/test_networks.py::test_address_invalid[foo tests/test_networks.py::test_address_invalid[foo@bar@example.com] tests/test_networks.py::test_address_invalid[\n@example.com] tests/test_networks.py::test_address_invalid[\r@example.com] tests/test_networks.py::test_address_invalid[\x0c@example.com] tests/test_networks.py::test_address_invalid[ tests/test_networks.py::test_address_invalid[\x1f@example.com] tests/test_networks.py::test_address_invalid["@example.com0] tests/test_networks.py::test_address_invalid["@example.com1] tests/test_networks.py::test_address_invalid[,@example.com] tests/test_networks.py::test_email_str tests/test_networks.py::test_name_email