Example $1$:

The fluid in Fig. $40$ is water, with the surface $20$ ft above the datum. The pipe is $6$ in$.$ in diameter, and the total loss of head between point $1$ in the water surface and point $5$ in the jet is $10$ ft$.$ Determine the velocity of flow in the pipe and the discharge Q$.$

In example $1$ above, assume the following head losses: from $1$ to $2,0$ ft; from $2$ to $3,2$ ft; from $3$ to $4,7$ ft; from $4$ to $5,1$ ft$.$ Make a table showing elevation head, velocity head, pressure head, and total head at each of the five points. How high above the center of the pipe will water stand in the piezometer tubes at $3$ and $4?$