There is a flowmeter device used to measure the flow rate of a filter.

Pressure gauges are attached to the upper sections of the piping at the water inlet $($Inlet$)$ to the filter and the discharge outlet $($Outlet$)$ from the filter, with the difference between these pressures being considered the differential pressure.

The overall structure of the flowmeter device consists of a continuous water flow system: water is pumped from a pump, passes through the flowmeter, goes through the filter$$s Inlet, exits through the Outlet, passes through a valve to adjust the flow rate, and finally returns to the pump.

Additionally, there are two flowmeter devices: Flowmeter Device A$,$ with a pipe length of $40$ cm from the Outlet, and Flowmeter Device B$,$ with a pipe length of $170$ cm from the Outlet. Both devices have the same inner pipe diameter.

If the pump pressure is the same for both Flowmeter Device A and Flowmeter Device B$,$ and the valve inside the pipe is adjusted to ensure the same differential pressure for both, and the flow rate is measured under these conditions, will the flow rate readings of Flowmeter Device A and Flowmeter Device B be the same?