- #1
Anachronist
Gold Member
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Bernoulli's equation gives us this as the flow rate from a pressurized tank:
$$v = C_v \sqrt{2gh + \frac{p}{\rho}}$$
where ##C_v## is the velocity coefficient, ##g## is the acceleration due to gravity, ##h## is the height of the water above the exit hole, ##p## is the excess pressure above ambient, and ##\rho## is the fluid density (1000 kg/m3 for water).
My problem is, the viscosity of water changes significantly with temperature... like, a factor of 2 difference between cold water and warm water.
Wouldn't that mean hot water would exit the tank faster than cold water, for the same pressure?
I would think, with such a large difference in viscosity between cold and hot water, I'd see a large difference in flow rate also. If I wanted to increase the mass flow rate without increasing pressure or hole size, it would seem that increasing the temperature of the water would accomplish that.
How would I calculate the flow velocity to account for temperature?
The velocity coefficient ##C_v## seems like a fudge factor that would account for viscosity. The Engineering Toolbox gives a value of 0.97 for water, but I suspect that this is for a specific temperature. And I haven't been able to find anything that helps me account for viscosity when calculating the flow from a pressurized tank.
$$v = C_v \sqrt{2gh + \frac{p}{\rho}}$$
where ##C_v## is the velocity coefficient, ##g## is the acceleration due to gravity, ##h## is the height of the water above the exit hole, ##p## is the excess pressure above ambient, and ##\rho## is the fluid density (1000 kg/m3 for water).
My problem is, the viscosity of water changes significantly with temperature... like, a factor of 2 difference between cold water and warm water.
Wouldn't that mean hot water would exit the tank faster than cold water, for the same pressure?
I would think, with such a large difference in viscosity between cold and hot water, I'd see a large difference in flow rate also. If I wanted to increase the mass flow rate without increasing pressure or hole size, it would seem that increasing the temperature of the water would accomplish that.
How would I calculate the flow velocity to account for temperature?
The velocity coefficient ##C_v## seems like a fudge factor that would account for viscosity. The Engineering Toolbox gives a value of 0.97 for water, but I suspect that this is for a specific temperature. And I haven't been able to find anything that helps me account for viscosity when calculating the flow from a pressurized tank.