$$P_1+\frac12\rho V_1^2+\rho gh_1=P_2+\frac12\rho V_2^2+\rho gh_2$$
$$V=Qt, \; Q=A\bar v$$
I have a tank of water in the garden and I am assuming it is full when I start watering. I'm using a couple different equations to see how quickly and how much water is flowing out of a fire hose to water trees. The hose itself is made out of polyester and it is 100 ft. long. When I open the valve, the hose doesn't become completely turgid, and so I'm thinking that there is some energy lost because of flow in the hose and the pressure necessary to keep the hose from collapsing. The flow isn't very great and so I'd like to see what I'm dealing with here so I can buy a smaller hose.
The hose right now is 2 in. (0.05 m) in diameter and the tank is 2 m high. I did some calculations to get the flow rate using the above equations, but I ended up with 6 m/s for velocity and 48 L/s for the flow rate, which is much higher rate than what I am actually experiencing. I am calculating the velocity as $$V_2=\sqrt{2\rho gh},$$ and I derived this by assuming that $$h_2 = 0,$$ $$P_1 - P_2 = 0, \; \text{and}$$ $$V_1 = 0,$$ but it doesn't seem quite right.