Whit a solar panel that feed the pump
direct you can get problem.
(The numbers are taken out of the air but are quite accurate.)
In the middle of the day the panel gives 14 V. That will the pump
2 h before and 2 h after midday the panel will give 12 V. That what the pump want.
4 h before and 4 h after midday the panel will give 8 V. That could be a problem. Maybe will the pump not rotate but it will take current
. That current
will make the pump hot, maybe so hot that it burns.
If you take the power from a small separate solar panel or from the big panels
you already have will not make any difference.
The finest solution (and most complicated) is to measure the temperatures both on the panel and in the tank. As long as the panel is warmer than the tank the pump should operate.
A simpler solution is to assume that the tank have a temperature of 40°C and have a thermostat that starts the pump when the panel gets over 40°C.
If you have a tank with warm water and mount a coil of pipe inside of that to get warm water for the shower
, you need a long pipe. To calculate the length is quite straight, the only figure that could be hard to find is how much power you can get over between the water inside the tube and the water in the tank. A realistic figure is 100 W/°C m². If you want so can I make a spreadsheet that helps you to calculate the length. But it will be with metric units.