Calculate the water pressure at the bottom of the 100-m-high water tower
lets look at a column of water 100m high, with cross section of 1m^2
weight of water= density water*volume water*average height
= 1E3kg/m^3*9.8N/kg*100m^3*50m
= 4.9E8N
pressure= weight/area= 4.9E8P or 4.9E5kpa
= 490 kpa or in atmospheres,
= 490/101 atmospheres
check my math.
well, let's say the density of water is 1000 kg/m^3.
Then the weight of 1 m^3 of water is 9810 Newtons
Then the weight of a stack of those 100 m high = 9,810,000 Newtons and that is the force down on a square meter of bottom above atmospheric (the "gage" pressure). A Newton per square meter of pressure is called a "Pascal".
To get the total pressure you must add the pressure of the air on the top of the stack (atmospheric pressure) which is about 10^5 or 100,000 Pascals
So the total pressure is about 9,910,000 or 10^7 Pascals
To calculate the water pressure at the bottom of a water tower, we can use the formula:
Pressure = Density × Gravity × Height
Where:
Density of water = 1000 kg/m³ (approximate value)
Gravity = 9.8 m/s² (approximate value)
Height = 100 m
Using these values, we can plug them into the formula to find the water pressure:
Pressure = 1000 kg/m³ × 9.8 m/s² × 100 m
Calculating,
Pressure = 980,000 pascal (Pa)
So, the water pressure at the bottom of the 100-meter-high water tower is approximately 980,000 Pa.
To calculate the water pressure at the bottom of a water tower, we can use the formula for pressure:
Pressure = Density of water × Acceleration due to gravity × Height
The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s². The height of the water tower is given as 100 meters.
Now, let's substitute the values into the formula:
Pressure = 1000 kg/m³ × 9.8 m/s² × 100 m
To simplify the calculation, we can cancel out the units:
Pressure = 1000000 kg m² / m³ s²
Simplifying further, we can convert kg m²/m³ s² to pascals (Pa), which is the SI unit of pressure:
1 Pa = 1 N/m²
Pressure = 1000000 N/m² or 1000000 Pa
Therefore, the water pressure at the bottom of the 100-meter-high water tower is 1,000,000 Pascals or 1 Megapascal (MPa).