forfully-developedturbulentflowinapipe-stfx（23页）.doc

For fully-developed turbulent flow in a pipe: where n varies from 6 to 10 depending on the flow Reynolds number and umax is the velocity on the pipe axis. Let n = 7 in most cases (1/7th power-law velocity distribution in fully-developed turbulent pipe flow) with n = 7 Flow along curved streamlines Fluid is accelerated both along the streamline (in the s-direction) and normal to the streamlines (in the n-direction) Velocity field: Accleration: (along streamline) Acceleration normal to the streamline: d? is small ( sin d??( d??????ds =Rd?; ds is small (second-order term) Water flows steadily up a vertical 0.1 m diameter pipe and out the nozzle, which is 0.05m in diameter, discharging to atmospheric pressure. The stream velocity at the nozzle exit must be 20m/sec. Calculate the gage pressure required at section (1), assuming frictionless flow. Given: Flow is steady Frictionless flow can be assumed Working fluid is water (Flow is incompressible From the foregoing, (Bernoulli’s equation can be applied along a streamline Central streamline is chosen Continuity: Water may be considered to flow without friction through the siphon. The water flow rate is 0.03m3/sec, its temperature is 20C, and the pipe diameter is 75 mm. Compute the maximum allowable height, h, so that the pressure at point A is above the vapor pressure of the water. Given: Flow without friction (frictionless flow Flow of water (incompressible flow Assume: Flow is steady ( Bernoulli’s equation can be applied along a streamline from (1) to (2) (since tank delivery pipe) (see handout) Continuity: The flow system of parallel disks shown contains water. As a first approximation, friction may be neglected. Determine the volume flow rate and the pressure at point (C). (R = 300mm and rc = 150mm.) Given: Flow of water (incompressible flow Friction may be neglected ( fric