Oil with density of 0.8505 and velocity of 4m/s in a pipe that has a downward slope of 1: 50 (sine). at a certain point in the pipe, a pressure gauge shows a pressure of 80kpa.
determine the pressure at a point 200m downstream of the gauge if:
(a) the flow losses are ignored (ideal case);
(b) there is a flow loss equal to 10% of the total initial head.

(a) Pressure at point 200 m downstream: 113.4 kPa

(b) Pressure at point 200 m downstream: 105.4 kPa

Explanation:

The point of reference, that will be named Point A, is the pressure gage.

The point 200 m downstream will be named Point B.

With a slope of 1:50, the height difference between A and B is (1/50)*200=4m.

(a) In the case there is no friction losses, we can write

Because ther is no change in the diameter of the pipe, V=constant.

Rearranging

Then we have an increase in of 33.4 kPa, and pressure in Point B (downstream) is:

(b) If we consider 10% of the total initial head as friction loss, we have

In this case the rise in pressure is 25.4 kPa, due to the friction losses.

The pressure at point B is

0.88m hope i am correct : )