The pressure in a water pigeon the ground floor of a building is4×10fifth pa but three floors up it is only 2×10fifth pa. What is the height between the ground floor and the third floor? The water pipe may be assumed to be stationary density of water is1.0×1.0cubed kg/m cubed

You mean water density = 1 * 10^3 kg/m^3

p lower = p upper + rho g h
(4-2) 10^5 newtons/m^2 = 1000 kg/m^3 * 9.81 m/s^2 * h

h = 2 * 10^2 / 9.81 = 200/9.81 = 20.4 meters (I doubt it)

To solve this problem, we can use the concept of hydrostatic pressure. The hydrostatic pressure in a fluid is dependent on its density (ρ), the acceleration due to gravity (g), and the height (h) of the fluid column.

The formula for hydrostatic pressure is given by:
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.

In this case, we are given the pressure at two different heights:
P1 = 4×10^5 Pa (ground floor)
P2 = 2×10^5 Pa (three floors up)

We can set up two equations using the formula for hydrostatic pressure.

Equation 1: P1 = ρgh1
Equation 2: P2 = ρgh2

Since the density of water is given as 1.0 × 10^3 kg/m^3 and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values in the equations.

Equation 1: 4×10^5 = (1.0×10^3) × 9.8 × h1
Equation 2: 2×10^5 = (1.0×10^3) × 9.8 × h2

Now, we can solve for the heights h1 and h2.

Solving Equation 1 for h1:
h1 = (4×10^5) / [(1.0×10^3) × 9.8]

Simplifying the equation:
h1 = 4 × 10^2 / (1.0 × 9.8)

Calculating the value of h1:
h1 ≈ 40.82 meters

Solving Equation 2 for h2:
h2 = (2×10^5) / [(1.0×10^3) × 9.8]

Simplifying the equation:
h2 = 2 × 10^2 / (1.0 × 9.8)

Calculating the value of h2:
h2 ≈ 20.41 meters

Now, the height between the ground floor and the third floor can be determined by calculating the difference between h1 and h2:

Height = h1 - h2
Height ≈ 40.82 - 20.41
Height ≈ 20.41 meters

Therefore, the height between the ground floor and the third floor is approximately 20.41 meters.