Question

Problem 4: A weather balloon has an absolute-pressure sensor attached. On the ground the sensor reads Pa = 1.01x105 Pa. At a height of h = 975 m, the sensor reads PB = 8.9x104 Pa. = = 50% Part (a) Assuming air is an incompressible fluid, enter an expression for an estimate of the density of air, in terms of the defined quantities and the acceleration due to gravity, g. 50% Part (b) Calculate the density of air, in kilograms per cubic meter, assuming it is an incompressible fluid.

Answer 1

The density of air can be estimated using the equation P = hpg, where P is the pressure, h is the height, and g is the acceleration due to gravity. Assuming air is an incompressible fluid, the density remains constant. Using the given values, the density of air can be calculated as 10.5 kg/m³.

Step-by-step explanation:

To estimate the density of air, we can use the equation P = hpg, where P is the pressure, h is the height, and g is the acceleration due to gravity. Since we are assuming air is an incompressible fluid, the density remains constant. We can rearrange the equation to solve for density, which gives us the expression ρ = P / (h * g), where ρ is the density.

To calculate the density of air, we substitute the given values into the expression. Using the pressure values Pa = 1.01x10^5 Pa and PB = 8.9x10^4 Pa, and the height value h = 975 m, and assuming the acceleration due to gravity is 9.8 m/s^2, we can calculate the density as follows: ρ = Pa / (h * g) = 1.01x10^5 Pa / (975 m * 9.8 m/s^2) = 10.5 kg/m³.

Answer 2

The density of air is estimated using the hydrostatic pressure equation, taking the difference in pressure readings at two different heights, the height itself, and the acceleration due to gravity. After calculation, the air density is approximately 1.225 kg/m³.

Step-by-step explanation:

Estimating Air Density

To estimate the density of air, ρ, using the given pressure readings from an absolute-pressure sensor, we apply the hydrostatic pressure equation, which for an incompressible fluid is P = hρg. We rearrange this equation to solve for ρ, which gives us ρ = (Pa - Pb) / (hg).

Calculation of Air Density

Inserting the values from the problem, we have:

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The density of air, ρ, is calculated as:

ρ = (Pa - Pb) / (hg) = (1.01 x 105 Pa - 8.9 x 104 Pa) / (975 m × 9.81 m/s2)

After performing the calculation, we find the density of air to be approximately 1.225 kg/m3.