The pressure at the lower end of the pipe is 32474.22 N/m².
To find the pressure at the lower end of the pipe, we can use the principle of hydrostatic pressure. Hydrostatic pressure is given by the equation 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 have a pipe with a slope of 1 in 30, which means that for every 30 units of horizontal distance, the pipe rises 1 unit in height. Therefore, the height difference between the upper end and the lower end of the pipe can be calculated by multiplying the length of the pipe by the slope.
Using the given information:
- Length of the pipe, l = 100m
- Diameter at the upper end, d1 = 600mm
- Diameter at the lower end, d2 = 300mm
- Rate of flow, Q = 50 liter/sec
- Pressure at the higher level, P1 = 19.62 N/cm²
We can calculate the height difference:
Height difference = l x slope
Plugging in the values:
Height difference = 100m x (1/30)
Height difference = 3.33m
Now, we can calculate the pressure at the lower end:
P2 = P1 + ρgh
Since the diameter at the lower end is smaller than the diameter at the upper end, the cross-sectional area of the pipe decreases. This means that the velocity of the fluid increases according to the principle of continuity. Therefore, we can assume that the density of the fluid remains the same at both ends.
Plugging in the values:
P2 = 19.62 N/cm² + (1000 kg/m³ x 9.8 m/s² x 3.33m)
P2 = 19.62 N/cm² + 32454.6 N/m²
P2 = 32474.22 N/m²