Assuming the fluid has a density of 1.00 (g/cm^) at what height h should the bottle be placed so the liquid pressure is 38mm-Hg ?
B.At what height h should the bottle be placed so the liquid pressure is 460mm-H_2O ?
C.If the blood pressure is 18 {mm-Hg} above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?
D(mercury)*P(mercury)=D(liquid)*h(liquid)
a)13.5*38=1*h do rest like this to
To answer these questions, we will use the principles of fluid pressure and the equation for hydrostatic pressure.
The hydrostatic pressure (P) at a certain height (h) 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 column.
Now let's solve each question:
A. To find the height (h) at which the liquid pressure is 38 mm-Hg, we need to convert the pressure from mm-Hg to the unit of pressure we are using:
1 mm-Hg = 13.6 g/cm² (approx.)
So, the pressure becomes:
P = (38 mm-Hg) * (13.6 g/cm²/mm-Hg) = 516.8 g/cm²
Now, rearranging the hydrostatic pressure equation, we can solve for h:
h = P / (ρg) = (516.8 g/cm²) / (1.00 g/cm³ * 9.8 m/s²)
Note: We need to convert the density from g/cm³ to kg/m³ and the acceleration due to gravity from m/s² to cm/s² to make the units consistent.
B. To find the height (h) at which the liquid pressure is 460 mm-H₂O, we need to convert the pressure from mm-H₂O to the unit of pressure we are using:
1 mm-H₂O = 0.098 kPa (approx.)
So, the pressure becomes:
P = (460 mm-H₂O) * (0.098 kPa/mm-H₂O) = 45.08 kPa
Now, rearranging the hydrostatic pressure equation, we can solve for h:
h = P / (ρg) = (45.08 kPa) / (1.00 g/cm³ * 9.8 m/s²)
C. To find the height (h) at which the fluid just barely enters the vein, considering an additional blood pressure of 18 mm-Hg above atmospheric pressure, we need to add this value to the pressure in the hydrostatic pressure equation:
P = (18 mm-Hg + atmospheric pressure) * (13.6 g/cm²/mm-Hg)
Now, rearranging the hydrostatic pressure equation, we can solve for h:
h = P / (ρg) = [(18 mm-Hg + atmospheric pressure) * (13.6 g/cm²/mm-Hg)] / (1.00 g/cm³ * 9.8 m/s²)
In each case, once you have calculated the value of h, you will know the height at which the bottle should be placed for the desired pressure.