why flow meter must be installed at the discharge of the pump?
The flow meter or circuit balance valve must be on the discharge side of the pump to ensure it does not negatively affect the operation of the pump. The pump can deal with a slight increase in discharge pressure much better than an increase in suction pressure.
In fact on a heating water system if intake is restricted the pressure can change enough to cause hot water to flash to steam. This will eat out the pump impellor causing the pump to fail.