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.

 

[DeeNos]

To calculate the mean velocity of the fluid from the power of the heater, you will need to use the principles of heat transfer and energy conservation. Here are the steps you can follow to approach this problem:

1. First, determine the amount of heat energy that is being transferred from the heater to the fluid. This can be calculated by multiplying the power of the heater (in watts) by the time it is turned on (in seconds). This will give you the total amount of heat energy (in joules) that is being supplied to the fluid.

2. Next, calculate the change in temperature of the fluid caused by the heat energy from the heater. This can be done by measuring the temperature of the fluid at the inlet and outlet of the heater. The difference between these two temperatures will give you the temperature rise (ΔT).

3. Now, use the specific heat capacity of water (4.186 joules/gram °C) to convert the temperature rise into the amount of heat energy absorbed by the fluid (Q = mCΔT, where m is the mass of the fluid).

4. Since the heat energy supplied by the heater is equal to the heat energy absorbed by the fluid, you can equate the two values and solve for the mass of the fluid (m = Q/CΔT).

5. Once you have the mass of the fluid, you can use the continuity equation (Q = ρAv, where ρ is the density of the fluid, A is the cross-sectional area of the circuit, and v is the velocity of the fluid) to calculate the mean velocity of the fluid.

6. You can also use Bernoulli's equation (P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2) to calculate the velocity of the fluid at the inlet and outlet of the heater and then take the average to get the mean velocity.

Keep in mind that these calculations may not be completely accurate as they do not take into account factors such as friction and turbulence in the fluid flow. However, they can give you a rough estimate of the mean velocity of the fluid in the circuit.