The maximum blood pressure in the upper arm of a healthy person is about 120 mmHg. If a vertical tube open to the atmosphere is connected to the vein in the arm of the person, determine how high the blood will rise in the tube. Take the density of the blood to be 1040 kg/m3. Express your answer in m.

Sure, let's break this down step by step:

1. First, we need to understand that the pressure at a certain depth in a fluid is given by the equation P = ρgh, where:

   • P is the pressure,
   • ρ is the density of the fluid,
   • g is the acceleration due to gravity, and
   • h is the height of the fluid above the point in question.

2. We want to find the height (h) to which the blood will rise in the tube. So, we can rearrange the equation to solve for h:

   • h = P / (ρg)

3. We know that the maximum blood pressure (P) is 120 mmHg. However, we need to convert this to a standard unit of pressure, which is pascals (Pa). 1 mmHg is approximately equal to 133.322 Pa, so 120 mmHg is approximately equal to 120 * 133.322 = 15998.64 Pa.

4. We also know that the density of blood (ρ) is 1040 kg/m3, and the acceleration due to gravity (g) is approximately 9.81 m/s2.

5. Now, we can substitute these values into the equation to find h:

   • h = 15998.64 Pa / (1040 kg/m3 * 9.81 m/s2)

6. If you do the math, you'll find that h is approximately 1.56 m.

So, the blood will rise to a height of approximately 1.56 m in the tube.