Derive the relation (Hagen-Poiseulle Law) for the head loss due to friction in Laminar flow case in pipes. Also prove that mean velocity Vis half of the maximum velocity for laminar flow case. Hint: consider a fluid element at a distance r' from the center of the pipe. Let 'd' be its thickness and 'dA' be its area.
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- Jet water in Pipe with diumeter equal to Somm to velocity=30 - divided into fwo branches with (o-756) ancd the o ther with Cu.25Q] recPcetively un equal diameter. Compute fore CumPenen ts on the Plate sec VュIn a pipe of diameter 300mm the center line velocity and the velocity at a point 100mm from the center, as measured by pitot tube are 2.4 m/s and 2.0 m/s respectively. Assume the flow in the pipe to be turbulent find: 1-Dischrge through the pipe,2-Coefficient of friction, 3 Height of roughness projections.Please do not waste my question solve with correct answers only.HW6_Question 2. Consider fully developed laminar flow in the annulus between two concentric pipes. The radius of the two pipes are ro and rj. The outer pipe is stationary, and the inner pipe moves in the x direction with speed Vo. Assume the axial pressure gradient is zero: %3D • Öx Obtain an expression for the velocity profile, u(r), and find out the value of u(r) in the middle of the annulus: (r = ) ro=2 cm, r;=1 cm, Vo = 0.3 m/s.
- Water (density 1000 kg/m?) flows through an inclined pipe of unform diametar. The velocity. pressura and elevation at section A are V, = 3.2 mis, p, =186 kPa and 2, = 245 m respectively, and those at section B ara V = 3.2 /s, py = 260 kPa and 2y = 9.1 m, respectivoly. If accaleration due 1o gravity /s 10 m/s* then the head lost due to friction is ‘m (round off 1o one decimal place).(350 L/min) of oil (r.d -0.9 and u -0.0574 Pa.s )flow through a pipe line 75 mm) in diameter .Calculate center line velocity, the head lost in ( 300 m) of this n and the shear stress and velocity at point ( 25 mm) from the center line.VIN/20 water is pumped from a * large tanken to a second tand 2 through a pipe system, as shown in the figure. The pump is developing on the flow. For a steady flow of 140 L/s, what must be the pressure PB in the air trapped above the water 20 kw . tank 2. The vertical 7.S pipe 40m Long. Фра=2 кра Solution Power: 20 kw Q = 140 L/S 150m 45m PB = ? h = 40m d=200mm = 0.2m M= 0.998X13 Nism OPB 6m B. E 1.42 ·lum water D=200 2 2 9u
- A necked-down section in a pipe flow, called a venturi,develops a low throat pressure that can aspirate fluidupward from a reservoir, as in Fig. UsingBernoulli’s equation with no losses, derive an expressionfor the velocity V 1 that is just sufficient to bring the reservoirfl uid into the throat.Calculate the available net positive section head NPSH in a pumping system if the liquid density p 1200 kg/m'. The liquid dynamic viscosity u 0.4 Pa.s, the mean velocity a= 1 m/s, the static head on the suction side z = 3m, the inside pipe diameter di, = 0.0526m. the gravitational acceleration g = 9.81 m/s, and the equivalent length on the suction side EL, = 5.0 m. The liquid is at its normal boiling point. Neglect entrance and exit 1 losses.A pipe of diameter 12 cm, is used to pump the water to the house in the Hamra hill at the height of 60 m than the ground. The discharge at the end of the pipe is 200 lit/s. The pressure gauge is fitted at the entry of the pipe in the ground is 34 N/cm?. Find the following: (i) The velocity head at the entry of pipe (in m) (ii) Pressure head at the inlet (in m) (iii) Total available energy per unit weight of the water at the pipe inlet (unit in m) (Enter only the values by referring to the units given in brackets & DO NOT write the unit & do not send the handwritten answers to my mail id...) velocity head at the entry of the pipe is = (unit in m) pressure head at inlet = (unit in m) Total available energy per unit weight of the water at inlet of the pipe
- A tanker carrying tolueneis unloaded to an onshore storage tank using the ship’s pumps. The pipeline is 225-mm inside diameter and 900-m long (200-m long suction line, 700-m long discharged line). Miscellaneous losses due to fittings, valves, etc., amount to 100 equivalent pipe diameters at the suction side, and 500 equivalent pipe diameters at the discharged side. The maximum liquid level in the destination storage tank is 30 m above the lowest liquid level in the ship’s tanks. The ship’s tanks are nitrogen blanketed and maintained at an absolute pressure of 1.05 bar (1 bar = 10^5 Pa). The storage tank has a floating roof, which exerts an absolute pressure of 1.1 bar on the liquid. The ship must unload 1000 metric tons within 5 hours. Taking pump efficiency as 70%, (ρ = 874 kg/m3, μ = 0.62 cP, Pvapor = 0.037 atm absolute). Determine: Discharge head (m) and pressure (Pa) Actual pump power (kW) Available NPSH (m)A tanker carrying tolueneis unloaded to an onshore storage tank using the ship’s pumps. The pipeline is 225-mm inside diameter and 900-m long (200-m long suction line, 700-m long discharged line). Miscellaneous losses due to fittings, valves, etc., amount to 100 equivalent pipe diameters at the suction side, and 500 equivalent pipe diameters at the discharged side. The maximum liquid level in the destination storage tank is 30 m above the lowest liquid level in the ship’s tanks. The ship’s tanks are nitrogen blanketed and maintained at an absolute pressure of 1.05 bar (1 bar = 10^5 Pa). The storage tank has a floating roof, which exerts an absolute pressure of 1.1 bar on the liquid. The ship must unload 1000 metric tons within 5 hours. Taking pump efficiency as 70%, (ρ = 874 kg/m3, μ = 0.62 cP, Pvapor = 0.037 atm absolute). Determine: D. Discharge head (m) and pressure (Pa) E. Actual pump power (kW) F. Available NPSH (m)A tanker carrying tolueneis unloaded to an onshore storage tank using the ship’s pumps. The pipeline is 225-mm inside diameter and 900-m long (200-m long suction line, 700-m long discharged line). Miscellaneous losses due to fittings, valves, etc., amount to 100 equivalent pipe diameters at the suction side, and 500 equivalent pipe diameters at the discharged side. The maximum liquid level in the destination storage tank is 30 m above the lowest liquid level in the ship’s tanks. The ship’s tanks are nitrogen blanketed and maintained at an absolute pressure of 1.05 bar (1 bar = 105 Pa). The storage tank has a floating roof, which exerts an absolute pressure of 1.1 bar on the liquid. The ship must unload 1000 metric tons within 5 hours. Taking pump efficiency as 70%, (ρ = 874 kg/m3, μ = 0.62 cP, Pvapor = 0.037 atm absolute). Determine: A. Pump head (m) B. Pump differential pressure (Pa) C. Suction head (m) and pressure (Pa) D. Discharge head (m) and pressure (Pa) E. Actual pump power…