//You can do simply Like This

using System;
using System.Data;
using System.Configuration;
using System.Web;
using System.Web.Security;
using System.Web.UI;
using System.Web.UI.WebControls;
using System.Web.UI.WebControls.WebParts;
using System.Web.UI.HtmlControls;

public partial class _Default : System.Web.UI.Page
{
protected void Page_Load(object sender, EventArgs e)
{

}
protected void btnSubmit_Click(object sender, EventArgs e)
{
string str;
str = txtString.Text;

int vowel = 0;
for (int n = 0; n < str.Length; n++)
{

switch (str[n])
{
case 'a':
case 'A':
vowel++;
break;
case 'e':
case 'E':
vowel++;
break;
case 'i':
case 'I':
vowel++;
break;
case 'o':
case 'O':
vowel++;
break;
case 'u':
case 'U':
vowel++;
break;
}
}
Response.Write(vowel);
}
}