I take it you're after something like
http://myapplication/
in order to access the project on your network. To that you're going to need to create custom
DNS[^] record to resolve the host name to an IP address.
You can either add a custom DNS record on each machine (which is probably going to be inconvenient), or you can setup them up in your DHCP server. The DHCP server will likely provide the DNS and usually there'll be options in there for configuring it, more than likely on your router. If you login to your router as an admin, try and find anything about LAN IP setup or DNS, and in there might be options for adding hostnames to local IP addresses.