A 300-mm pipe carries oil of so gr 0.812 at a rate of 0.111 m³/s, and the pressure at a point A is 18.4 kPa gage. If point A is 1.89 m above the datum plane, calculate the energy at A.

Problem Consider a cylindrical pipe of length L and diameter D = 2R. The angle that the axis of the pipe forms with the vertical direction is a. Assume that when the fluid enters the pipe its velocity is uniform (i.e., it has the same value over the entire cross-section of the pipe) and equal to U in the axial direction. In the radial and angular directions, the velocity is zero. So, it is: 2 =0: v(r, 0, 2) = Ue, (1.1) Here v is the fluid velocity and e, is a vector of unit magnitude parallel to the coordinate axis z; furthermore, we have assumed that the pipe inlet is located at z = 0. Near the entrance of the pipe, the velocity profile varies in the axial direction. But after a certain entrance length, the profile becomes fully developed, no longer changing with z. The evolution of the velocity profile is sketched in Fig. 1, where, for clarity, the pipe inclination is not shown. The entrance length is denoted by L.. For z > L., the fluid velocity is no longer a function of the axial…

The turbine at C draws a power P kW. If the intake B has a diameter of de mm. The pressure dg(mm) dĄ(mm) at the intake B is Ps kPa and the velocity of the water (density = 1kg/L) at that point is v (m/s). The frictional losses between A and B are At neglected, and the exit A has a diameter of da B1 mm. Consider the data in the table to M = last two digits of your student ID P (kW) = 0.5M + 68.5 da(mm) = M + 150 dp (mm) %3D М + 400 PB (kPa) = M + 380 v (m/s) = 0.1M + 4 a- Calculate the velocity at the exit A b- Calculate the discharge at the exit A c- Calculate the turbine head d- Calculate the pressure at A m=13