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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…

An elbow deflects water upward and discharges it to the atmosphere at a specific rate. Determine the gage pressure at the inlet of the elbow and the anchoring force needed to hold the elbow in place. (gage pressure at the outlet is zero)

In a container of diameter Φ (see image), a tube of diameter ε (much smaller than the diameter of the container) is connected at a height d. The water level in the container is h. Water flows at a constant speed in the tube. The density of the fluid is ρ. If the container is open to the air, calculate the pressure at the connection. Conceptual question: In the second figure of the image, three pressures are represented. Are these pressures constant along the height they describe?