4. A pipe carries oil of density 800 kg/m³. At a given point (1) the pipe has a bore area of 0.005 m² and the oil flows with a mean velocity of 4 m/s with a gauge pressure of 800 kPa. Point (2) is further along the pipe and there the bore area is 0.002 m² and the level is 50 m above point (1). Calculate the pressure at this point (2). Neglect friction. (374 kPa)

Water flows steadily through a horizontal 30 degree pipe bend. At the inlet point 1, the diameter is 0.3 m, the velocity is 12 m/s, and the pressure is 128 kPa gauge. At the outlet point 2, the diameter is 0.38 m and the pressure is 145 kPa gauge. Determine the forces F_x and F_y necessary to hold the pipe stationary.

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…

What must the gauge pressure p be at A if the volume flow rate out of the pipe at point B is 0.0800 m^3/s?

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4. The velocity profile of a viscous liquid flowing over a fixed plate is given by v=0.68y-y² (v is the velocity in m/s and y is the distance from the plate in m). i. Calculate the shear stresses at the plate surface and 0.34 m away from the plate (u=0.9 Ns/m3). ii. Draw the velocity and the shear stress profile of the system. direction of flow plate

A pipe tapers over 60m from 450mm in diameter to 675mm in diameter. The gauge pressure at the inlet is 75 kN/m2 and the gauge pressure at the outlet is 90 kN/m2. If the centreline of the pipe rises at a gradient of 1 in 80 and the energy loss due to friction is 0.01m per metre length determine the flowrate in the pipeline and the velocity at entry and exit.

Water flows through a constricted pipe at a uniform rate. At one point, the diameter of the pipe is 0.056 m and the pressure is 5.7 x 104N/m2. At another point, 0.8 m higher than the previous point, the diameter is 0.023 m and the pressure is 1 X 104N/m2 . Calculate the velocities at the lower section and the upper section. Also calculate the rate of flow. Density of water = 1000 kg/m3.

Water (ρ = 1000 kg/m3) is flowing vertically in the pipe shown below. The top, middle, and bottom parts have radii of r1 = 3 cm, r2 = 1 cm, and r3 = 3 cm, respectively. The speed of water flow and the gauge pressure at point 1 are v1 = 20 cm/s and P1 gauge = 200 Pa. The height difference between point 1 and 2, point 2 and 3 is 10 cm.  Use g = 10 m/s2 for the acceleration due to gravity. What is the speed of the water flow at point 2? What is the gauge pressure at point 2? What is the speed of the water flow at point 3? What is the gauge pressure at point 3?

Find an expression for the velocity of water leaving the sprinkler. Find an expression for the gauge pressure at point A, a distance L1, upstream of the narrow pipes. Express the answer in terms of the flowrate, Q. The inner diameter of the first segment of the pipe is d1=10mm, the inner diameter of the second set of pipes is d2=1mm, with N=25. The flowrate through the sprinkler is Q=0.2 L/s. Flow in pipes typically becomes turbulent when the Reynolds number exceeds 2000. Comment on the accuracy of the assumption that the flow could be treated as laminar everywhere. May be assumed water has a density of 1000kg/m^3 and a viscosity of 1mPa s.