Calculating Velocity of a fluid (by thermal convection) from the heater power.

[Igloo_Boobs]

Ok, I have some questions to answer for this lab report, and one of them has left me clueless. The experiment was as follows:

An apparatus is made of a rectangular circuit (of known dimensions) of tubes filled with water with thermometers visible at various points throughout the circuit. No water can enter or leave the circuit, only flow around it. The driving force for this is the convection caused by a heat exchanger at the top of one side of the circuit and an electric heater (of known power) at the bottom of the other side.

I have to calculate the mean fluid velocity in three ways.

The first was to simply inject some dye and measure the time taken.

The second was a theoretical calculation using Reynolds and Grashof numbers and what have you.

The third is the one I'm struggling with. Word for word it says "Calculate the mean velocity from the electrical power supplied to the heater and the consequent temperature rise across the heater."

Anyone got any ideas how I could go about part three?

I'm fine with the rest of it, I just have no idea how to appoach part three. I suspect Bernoulli or continuity equations may be involved, and I also think I'm not taking into account some vital piece of information.

TL: DR how can I calculate the velocity of a fluid in a circuit from the power of the heater?

 

[RTW69]

This looks like a conservation of energy problem. You can assume that most of the power is converted to heat. That will be the energy added to the system. What heat not convected away from the module will increase the velocity of the fluid, neglecting pressure of height differences between the inlet and outlet.

 

[edgepflow]

...The third is the one I'm struggling with. Word for word it says "Calculate the mean velocity from the electrical power supplied to the heater and the consequent temperature rise across the heater."

Anyone got any ideas how I could go about part three?

TL: DR how can I calculate the velocity of a fluid in a circuit from the power of the heater?

An energy balance across the heater yields:

heater power = mass flow rate X specific heat X temperature rise across the heater

Solve for mass flow rate. The mass flow rate is related to velocity as:

mass flow rate = density X velocity X cross sectional area of flow

Solve for velocity.

 

[Igloo_Boobs]

That's it! That's exactly what I needed. Thanks so much.