File upload HTTP POST

I'm trying to upload a file through the HTTP POST.

I use the following components:

WebFilePicker1
WebFileUpload1
WebHttpRequest1
WebButton1

I don't like the appearance of the WebFileUpload1, so I put its property Visible to false.

In the OnChange event of the WebFilePicker1 I put the following code:

WebFilePicker1.Files[0].GetFileAsText;

and in its OnGetFileAsText event I put the code:

var
  myFile: TFile;
begin
  myFile:= WebFileUpload1.Files.Add;
  myFile.Name := webfilepicker1.Files[0].Name;
  myFile.Size := webfilepicker1.Files[0].Size;
  ...
  
I set the following properties of WebHttpRequest1:

Command=httpPOST
Headers=Content-Type=multipart/form-data
URL=http://myserver/upload

Finally in the OnClick event of WebButton1 I put the code:

WebHttpRequest1.PostData := 'uplodFile=' + WebFileUpload1.Files[0].Name;
WebHttpRequest1.Execute;

The server replies with an error, because the uploadFile is undefined. Nevertheless the following HTML code works well with the same server:
 
<html>
  <body>
    <form ref='uploadForm' 
      id='uploadForm' 
      action='http://myserver/upload' 
      method='post' 
      encType="multipart/form-data">
        <input type="file" name="uploadFile" />
        <input type='submit' value='Upload!' />
    </form>     
  </body>
</html>

What am I doing wrong?