calculate the absolute pressure at lusaka 1200 m above sea level where a pipe carrying water tapers from cross section of 0.3 m2 to 0.15m2 at B. At A the velocity, assumed uniform is 72 km/h and the pressure 65.60 m gauge. if the friction effects are negligible determine the pressure at B which is 6 m above the sea level of A and calculate the absolute pressure at A and B.
To calculate the absolute pressure at a certain location, we need to consider the effects of both the pressure due to the column of water above that location (hydrostatic pressure) and the pressure due to the velocity of the water (dynamic pressure). Here's how you can calculate the absolute pressure at point A and point B:
1. Calculate the absolute pressure at point A:
- Given that the pressure at A is 65.60 m gauge, we need to convert it to absolute pressure by adding the atmospheric pressure. Standard atmospheric pressure at sea level is approximately 101,325 Pascal (Pa).
- Absolute pressure at A = Gauge pressure at A + Atmospheric pressure
= 65.60 m + 101325 Pa
2. Calculate the velocity at point A:
- Given that the velocity at A is 72 km/h, we need to convert it to meters per second (m/s). Since 1 km/h is equal to 0.2778 m/s, the velocity at A is 72 km/h * 0.2778 m/s = 20 m/s.
3. Calculate the absolute pressure at point B:
- Given that point B is located 6 m above the sea level of A, we can use the hydrostatic pressure equation to find the difference in pressure due to the change in height.
- Change in pressure due to height difference = Density of water * g * change in height
- The density of water is approximately 1000 kg/m³, and g is the acceleration due to gravity (approximately 9.81 m/s²).
- Change in pressure due to height difference = 1000 kg/m³ * 9.81 m/s² * 6 m
4. Calculate the dynamic pressure at point B:
- The dynamic pressure can be calculated using the Bernoulli's equation, which states:
Dynamic pressure = (Density of water * velocity^2) / 2
- The density of water is 1000 kg/m³, and the velocity at B can be determined using the continuity equation. Since the cross-sectional area at B is given as 0.15 m², we can calculate the velocity at B as:
Velocity at B = (Area at A / Area at B) * Velocity at A
= (0.3 m² / 0.15 m²) * 20 m/s
5. Calculate the absolute pressure at point B:
- Absolute pressure at B = Absolute pressure at A + Change in pressure due to height difference + Dynamic pressure at B
By following these steps, you should be able to calculate the absolute pressure at points A and B based on the given information.