Why does the flowmeter reading increase when the control valve is partially closed or flow is reduced?

This is usually because the sensor is installed too close to the downstream of the control valve. When the valve is partially closed, the flowmeter actually measures the increased flow velocity caused by the reduced diameter of the valve. The solution is to move the sensor away from the control valve—install it 30 times the pipe diameter upstream of the control valve, or relocate it 5 times the pipe diameter upstream of the control valve.