Display div if option is selected in jQuery

when changing select box you can fadeIn elements that you want :

$('#graph_select').change(function(){
   var divID = $(this).children('option:selected').attr('id');
   if(divID == 'pilot_form'){
       $('#client_graph_form').fadeOut(1000,function(){
           $('#pilot_graph_form').fadeIn(500);
       });
   }else{
       $('#pilot_graph_form').fadeOut(1000,function(){
           $('#client_graph_form').fadeIn(500);
        });
   }
});

Updated
in other way : it will be better if you use same name with div's id name in options :

<select id="graph_select">
    <option class="pilot_graph_form">Pilot Hours</option>
    <option class="client_graph_form">Client Hours</option>
</select> 

add same class to each <div>

<div id="client_graph_form" class="forms"
...
<div id="pilot_graph_form" class="forms"

jQuery :

$('#graph_select').change(function(){
   var divID = $(this).children('option:selected').attr('class');
   $('.forms').fadeOut(1000,function(){
        $('#'+divID).fadeIn(500);
   });
});

$(function() {
  $("#graph_select").change(function() {
    if ($("#pilot_form").is(":selected")) {
      $("#pilot_graph_form").show();
      $("#client_graph_form").hide();
    } else {
      $("#pilot_graph_form").hide();
      $("#client_graph_form").show();
    }
  }).trigger('change');
});

DEMO

First of all, you should change "id" on your "option" to "value".

Then you can use this:

$(function () {
  $("#graph_select").change(function() {
    var val = $(this).val();
    if(val === "pilot_form") {
        $("#pilot_graph_form").show();
        $("#client_graph_form").hide();
    }
    else if(val === "client_form") {
        $("#client_graph_form").show();
        $("#pilot_graph_form").hide();
    }
  });
});