I have a small water pump to water my flowers. To control it, I want to know how much power is used. So I put it in a jar and powered it on. Pump I connect the pump to my bench power supply and test:

Voltage Amps Watts Remark
3.3 0.33 1.1 Slow, but working
5 0.43 2.1 Already ok
6.6 0.57 3.8 Good flow
8.4 0.77 6.4 Even more flow
10 0.97 9.7 Strong flow
12 1.25 15.0 Very strong flow

The flow seems to increase exponentially with the voltage and is corresponding with the Wattage. Since my project uses li-ion batteries which can provide 6.6 to 8.4 volts with 2 batteries the flow is ok, but not too strong. Maybe another battery would be an idea to increase the voltage to 9.9-12.6 volts.
On the other hand my batteries are solar powered and should therefore have enough power when the weather is nice and more water is needed.

I will use a IRLD024 mosfet which can switch 1.8 amps to control the pump since the relay was not reliable enough and drained too much power.