Question

What is the pressure at the bottom of a tank 1-m deep? Take the density of water to be 1000-kg/m^3, and gravitational acceleration to be 9.8-m/s^2. Enter your answer in N/m^2.

Answer 1

The pressure at the bottom of a 1-meter deep tank of water is 9800 N/m² or 9800 Pascals, calculated using the formula p = ρgh with the given density of water and gravitational acceleration.

Step-by-step explanation:

The pressure at the bottom of a tank that is 1 meter deep can be calculated using the formula p = ρgh, where p is the pressure, ρ (rho) is the density of the liquid, g is the acceleration due to gravity, and h is the depth of the liquid. Given the density of water is 1000 kg/m³ and the gravitational acceleration is 9.8 m/s², the pressure at the bottom of the tank can be calculated as:

Pressure p = (1000 kg/m³)(9.8 m/s²)(1 m) = 9800 N/m².

Thus, the pressure at the bottom of a 1-meter deep tank of water is 9800 N/m², which is also equivalent to 9800 Pascals (Pa) as 1 Pa = 1 N/m², verifying that hρg has units of N/m².

Answer 2

To solve this problem we will use the concepts related to hydrostatic pressure. Which determines the pressure of a body at a given depth of a liquid.

Mathematically this can be described as

`P= \rho gh`

Here

`\rho` = Density

g = Gravity

h = Height (Depth)

If we replace the values given in the equation we will have to

`P = 1000 (9.8)(1)`

`P = 9800 Pa`

Therefore the pressure at the bottom will be 9.8kPa