Question

one important function of cartilage tissue is to support force between bones of the body. to culture cartilage tissue in vitro, in a laboratory setting, a biomedical engineer wants to recreate the pressure forces that cartilage cells experience in the body. the engineer uses a column of static fluid (see figure below) to recreate physiological forces by varying the fluid above the tissue to create pressure. approximately up to 0.5 m of fluid can fill the column. if you use water as the fluid, how high would you fill the column to get a pressure of 105 kpa? what could you do to simulate a pressure of 110 kpa in the column shown?

Answer 1

To achieve a pressure of 105 kPa with water, a height of 10.7 meters is needed, which is not possible within the 0.5 m column limit. To simulate pressures like 110 kPa, one could use denser fluids or engineer a pressurized system.

Step-by-step explanation:

To simulate the physiological pressures cartilage cells experience in the body, engineers can use a column filled with fluid. The pressure exerted by a static fluid in a column can be calculated using the formula $P = \rho gh$, where P is pressure, $\rho$ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the fluid column. Given that the density of water is $1000 kg/m^3$ and standard gravity is $9.81 m/s^2$, we can solve for h to find the column height necessary to create a specific pressure.

For a pressure of 105 kPa, we have:

105,000 Pa = (1000 kg/m^3)(9.81 m/s^2)h

h = 105,000 / (1000 * 9.81)

h ≈ 10.7 meters

To achieve a pressure of 105 kPa, we would need to fill the column to approximately 10.7 meters with water, which exceeds the 0.5 m limit. To simulate higher pressures like 110 kPa in a static fluid column that has a maximum fill height limit, engineers can either increase the density of the fluid or apply an external force to the column. One approach might be to use a denser fluid such as a saline solution or to engineer a pressurized system.