A pump is installed in the basement of a 10-storey building in order to supply the occupants with water. Each storey is 3m high.
How much pressure must the pump exert on the water so that the water reaches the 10th floor with a pressure of 400 kPa?
400*10^3 Pa + (rho)(g)*(30 m)
"rho" is the density of ewater, 1000 kg/m^3
g = 9.8 m/s^2
Required Pump Pressure = (400 + 294) kPa
thank you very much
To solve this problem, we need to calculate the total pressure required at the basement in order for the water to reach the 10th floor with a pressure of 400 kPa.
Pressure is defined as force per unit area, and in this case, we need to consider the height difference between the basement and the 10th floor.
First, let's calculate the height difference between the basement and the 10th floor:
The building has a total of 10 storeys, and each storey is 3m high. So, the total height difference is 10 storeys * 3m/storey = 30m.
Next, we need to convert the desired pressure of 400 kPa into Pascals. 1 kPa is equal to 1000 Pa, so 400 kPa is equal to 400,000 Pa.
Now, we can calculate the total pressure required at the basement:
The pressure at the basement is equal to the atmospheric pressure plus the pressure due to the height difference.
Since we are given the pressure at the 10th floor (400,000 Pa), we can assume that the pressure at the basement is equal to the atmospheric pressure, which is approximately 101,325 Pa.
Therefore, the total pressure required at the basement is:
Total Pressure = Atmospheric Pressure + Pressure due to height difference
= 101,325 Pa + 400,000 Pa
= 501,325 Pa
So, the pump must exert a pressure of 501,325 Pa on the water in order for it to reach the 10th floor with a pressure of 400 kPa.