Relationship between Flow Rate and Vessel Diameter, Length, and Fluid Viscosity.
Lab07-Elvis-experiment
This experiment consisted of three different experiments. The first, was to find the relationship between the radius of the blood vessel and the flow of blood through the vessel. For this experiment, we used four tubes all with a different diameter (see table 1 for measurements), 1000ml beaker, 100 ml graduated cylinder, and a ring stand with clamps. The same procedure was used for all four tube radius tests. We took the tube with the funnel and placed it in the single stand. Next, we used the graduated cylinder and filled it up with water (See table 1 for water measurements). We then placed the tube over the beaker making sure the tube was at correct angle for the water to flow properly. Note, if the angle of the tube is off, the results are not going to be accurate. Three people were required to execute this experiment. The first person was needed to hold the tube in place and cover one end of the tube with their finger, the second kept time and data, and the third added water to the funnel so it can go through the tube. To start the experiment, the first person added water slowly to the funnel so it could fill the tube. The second person kept the tube at the right angle and plugged it with their finger while it filled with water. The beaker was placed at the end of the tube to catch the water that flows out. Make sure the tube does not contain any air bubbles or the results will not be accurate. Once the tube was filled with water, the second person removed their finger from the end that’s on the beaker and allowed the water to flow out. While this was going on the first person poured the 100 mL of water slowly into the funnel so it could go down the tube. The third person kept time on how long it took the water to flow out of the tube into the beaker and recorded it (See tables raw data). The raw data gathered from the experiment was then used to calculate the average time it took for the water to flow through the tubing. With these average times, you can now convert the raw data
(how many seconds it took for 100ml to flow through the tubing, e.g. 6.67 seconds; see sample equation below) into flow rate in L/min:
Flow Rate Formula:
Flow Rate= (100ml) (1L) (60s) = 0.90 L
(6.67sec) (1000ml) (1min) = min
Experiment 1.
The purpose of the first experiment was to find the relationship between the diameter of the tube and the flow rate.
Table 1: Raw data for diameter.
| Diameter (mm) | Water(mL) | Time (sec) | |||
| 1st | 2nd | 3rd | |||
| Tube 1 | 4 | 100 | 9.45 | 9.36 | 9.32 |
| Tube 2 | 5 | 100 | 5.41 | 5.52 | 5.17 |
| Tube 3 | 6 | 100 | 4.61 | 4.68 | 4.93 |
| Tube 4 | 10 | 100 | 2.67 | 2.81 | 2.75 |
Tube 1:
Average time = (5.79 + 5.12 + 5.30) / 3 = 5.40 sec
Flow rate = 100 mL / 5.40sec * 60sec / 1min * 1L/1000mL = 1.11 L/min
Tube 2:
Average time = (6.17+5.40+5.33) / 3 = 5.63 sec
Flow rate = 100ml/5.63sec * 60sec/1min * 1L/1000mL = 1.07 L/min
Tube 3:
Average time = (6.69+6.77+6.25) / 3 = 6.57 sec
Flow rate = 100mL/6.57sec * 60sec/1min * 1L/1000mL = 0.91 L/min
Tube 4:
Average time = (6.74+6.46+7.85) / 3 = 7.02 sec
Flow rate = 100mL/7.02 sec * 60sec/1min * 1L/1000mL = 0.85 L/min
Table 2: Diameter vs flow rate.
| Diameter (mm) | Water (mL) | Average time (sec) | Flow Rate (L/min) | |
| Tube 1 | 4 | 100 | 9.38 | 0.64 |
| Tube 2 | 5 | 100 | 5.37 | 1.12 |
| Tube 3 | 6 | 100 | 4.74 | 1.27 |
| Tube 4 | 10 | 100 | 2.74 | 2.19 |
Graph 1: Diameter vs flow rate.
Summary.
The diameter of the blood vessel is directly proportional to the flow rate. As the diameter of the vessel increases, the flow rate increases. Table 1 shows the relationship between diameter (mm) and the flow rate. The graph drawn from this data indicates a positive relationship between the diameter and flow rate. As the diameter of the tube increases, the flow rate increases as well. This model implies that as the diameter of the blood vessel increases, the flow rate of blood rises, and the heart is expected to work less.
Experiment 2
The purpose of the second experiment was to determine the relationship between the length of the tube and the flow rate.
Table 3: Raw data for length.
| Length (cm) | Water(mL) | Time (sec) | |||
| 1st | 2nd | 3rd | |||
| Tube 1 | 20 | 100 | 5.79 | 5.12 | 5.30 |
| Tube 2 | 40 | 100 | 6.17 | 5.40 | 5.33 |
| Tube 3 | 60 | 100 | 6.69 | 6.77 | 6.25 |
| Tube 4 | 80 | 100 | 6.74 | 6.46 | 7.85 |
Calculations
Tube 1
Average time = (5.79+5.12+5.30) / 3 = 5.40 sec
Flow rate = 100ml/5.40sec * 60sec/1min * 1L/1000mL = 1.11 L/min
Tube 2
Average time = (6.17 + 5.40 + 5.33) / 3 = 5.63 sec
Flow rate = 100ml/5.63 sec * 60sec/1min * 1L/1000mL = 1.07 L/min
Tube 3
Average time = (6.69 + 6.77 + 6.25) / 3 = 6.57 sec
Flow rate = 100mL/6.57sec * 60sec/1min * 1L/1000mL = 0.91 L/min
Tube 4
Average time = (6.74+6.46+7.85) / 3 = 7.02 sec
Flow rate = 100mL/7.02sec * 60sec/1min * 1L/1000mL = 0.85 L/min
Table 4: Length vs flow rate.
| Length (cm) | Water (mL) | Average time (sec) | Flow Rate (L/min) | |
| Tube 1 | 20 | 100 | 5.40 | 1.11 |
| Tube 2 | 20 | 100 | 5.63 | 1.07 |
| Tube 3 | 60 | 100 | 6.57 | 0.91 |
| Tube 4 | 80 | 100 | 7.02 | 0.85 |
Graph 2: Length vs flow rate.
Summary
The table above shows the relationship between the length of the tube (cm), and the flow rate of the fluid. The length of the vessel is inversely proportional to the flow rate. As the length increases, the flow rate decreases. The graph indicates a negative relationship between the length and flow rate. As the length of the tube increases, the flow decreases. This model indicates that the length of the blood vessel affects the flow rate of blood, such that as the vessel length increases, the heart needs to work more to pump the blood.
Experiment 3
The aim of third experiment was to determine the relationship between the percentage of syrup, and the flow rate.
Table 5: Raw data for viscosity.
| Syrup (mL) | Water(mL) | Time (sec) | |||
| 1st | 2nd | 3rd | |||
| Tube 1 | 30 | 70 | 6.56 | 6.79 | 6.65 |
| Tube 2 | 60 | 40 | 11.42 | 11.64 | 11.52 |
| Tube 3 | 80 | 20 | 38.75 | 39.51 | 46.43 |
Calculations
Tube 1
Average time = (6.56+6.79+6.65) / 3 = 6.67 sec
Flow rate = 100ml/6.67sec * 60sec/1min * 1L/1000mL = 0.90 L/min
Tube 2
Average time = (11.42+11.64+11.52) / 3 = 11.53 sec
Flow rate = 100mL/11.53sec * 60sec/1min * 1L/1000mL = 0.52 L/min
Tube 3
Average time = (38.75+39.51+46.43) / 3 = 41.56 sec
Flow rate = 100mL/41.56mL * 60sec/1min * 1L/1000mL = 0.14 L/min
Table 6: Viscosity vs flow rate
| Syrup (mL) | Water (mL) | Average time (sec) | Flow Rate (L/min) | |
| Tube 1 | 30 | 70 | 6.67 | 0.90 |
| Tube 2 | 60 | 40 | 11.53 | 0.52 |
| Tube 3 | 80 | 20 | 41.56 | 0.14 |
Graph 3: Viscosity vs flow rate
Summary:
Table 6 shows the relationship between the viscosity in terms of the percentage of syrup and the
Flow rate. Graph 3 indicates an inverse relationship between the viscosity given as % of syrup and the flow rate. This relationship implies that as the viscosity of blood increases, resistance to flow rises and the heart has worked more to pump the blood.
Letter to Elvis
The body needs sufficient blood and most importantly, the flow should be constant in all parts. To ensure there is a constant flow of blood, the heart must be able to push the blood with less resistance. Resistance to the flow of blood may result from several factors, including and not limited to what the experiment was about. In this case, therefore, the results are significant in helping reduce the workload of the heart, and especially with a weak heart.
The experiment indicates a significant relationship between the flow rate, and the blood vessel diameter, the length, and the viscosity (%syrup). As the graph shows, when the diameter of the blood vessel increases, it makes it easier for the heart to pump blood throughout the body with less resistance (Zamir, 2006, p. 27). With a smaller diameter, the heart must maintain a high pressure to ensure the flow is constant and reaches all organs. Secondly, the length of the blood vessel is inversely proportional to the flow rate of blood. With a longer vessel, the heart must pump blood at high pressure to ensure sufficient flow to the peripheral organs and tissues. Lastly, the inverse relationship between the flow rate and viscosity means the thinner the blood is, the easier it is for the heart to pump with less resistance (Biswas, 2002, p. 54).
It is clear that the three factors do have a significant effect on the blood flow, but the magnitude of this impact differs in each. To ensure sufficient flow of blood and less workload for the heart, increasing the vessel diameter and/or reducing the blood viscosity can be good actions. Adopting either of these measures requires selecting whoever action carries fewer negative effects and more positive effects on the body.
Recommendation
The best action to take is to focus on increasing the diameter of the blood vessels. The diameter of a blood vessel is determined by several factors. One such factor is the presence of anatomical variations, mechanical obstruction of the vessel lumen through arteriosclerosis that is a direct effect of excess cholesterol. Cholesterol increases in the blood either because of excess weight or consuming excess carbohydrates. Cholesterol coats the inner lining of blood vessels, causing a decrease in the diameter and eventually more resistance to blood flow. The following can help reduce cholesterol:
- Focus on eating more monounsaturated fats such as avocados and nuts.
- Avoid foods with trans fats such as cookies and pastries.
- Eat soluble fiber.
- Exercise to improve physical fitness, reduce weight, and reduce the harmful cholesterol in the body.
References
Biswas, D. (2002). Blood flow models: A comparative study. Mittal Publications.
Zamir, M. (2006). The physics of coronary blood flow. Springer Science & Business Media.
