Head loss due to friction free essay sample

1. To determine the head loss and friction factor for laminar turbulent flow in a smooth pipe over a range of Reynoldss number . 2. To obtain the following relationships : a. Head loss as a function of the velocity of flow . b. Friction factor as a function of Reynolds number . Theory : The friction resistance to the flow of fluid through a pipe results in a loss of pressure energy for a given fluid flowing a long a given pipe, experiments show that for laminar flow : Hl ? V And for turbulent flow : Hl ? Vn Where : Hl :is the loss of pressure head . V : the mean velocity of flow . n : an index that lies between ( 1. 7 – 2. 0 ) depending on Reynolds number ( Re ) and on the roughness of the pipe wall. The Reynolds number ( Re ) is given by : Re = ( ?. V. d /? ) ( 1 ) Where : d = pipe diameter ? = fluid density ? = absolute viscosity In engineering practice, it is customary to use Darcys equation to express the pressure head loss as follows : hL = h 1 – h 2 = 4 ( L / d ) ( V2 / 2g ) - ( 2 ) Where : h1 h2 : static heads at two points in the pipe L = distance between h1 h2 f = fexp. : experimental friction factor which varies with Re and pipe roughness . Blasius has shown that a line whose equation is may closely approximate the friction factor Reynoldss number relationship for turbulent flow : ftheo. = ( 0. 079 /Re0. 25 ) ( 3 ) For laminar flow condition ,the Hagen-Poiseurlle law yields the relation : ftheo. = ( 16 / Re ) ( 4 ) Apparatus : The laminar / turbulent pipe flow apparatus consist of a circuit through which the fluid is circulated continuously by means of gear pump . the selected fluid is oil of a suitable viscosity to give values of Re well down into the laminar region. It is drawn from the reservoir and delivered by way of the lower horizontal pipe to the Perspex – settling chamber. The oil passes from this chamber through a bell mouth into the upper horizontal pipe in which the observations are taken. This pipe is of ( 19 mm) bore and have over all length about ( 6 m ) ,with an adjustable flow disturber upstream of the pipe to induce turbulence to the flow . Eighteen pressure taping permit determinations of pressure gradient . traverses with total head tubes in two directions at right angles in a common transverse plane, near the down stream end ,give the velocity profile . on leaving the pipe the oil , on it’s way to the weighing tank ,passes through a Perspex deflector in which the discharge may be observed. After being weight the oil flows back into the reservoir . the flow quantity is varied by means of an adjustable by-pass value . Procedure : 1. The apparatus was run for a few minutes to make sure that the motor was warmed up and steady conditions were ensured . 2. The two pitot traverse heads were with drawn and air was bleeded from the settling chamber and from all the manometers to avoid errors in pressure measurement . 3. The readings of the manometer connected to the pressure tapping No. ( 10 18 ) were record , and the flow rate was measured by timing the collection of oil in the weighing tank . 4. For each type of flow the pass values were used to tank a series of some readings for the pressure head loss and the flow rate . NOTE : A mercury manometer measure pressure in the apparatus . Thus corresponding head of oil is : hm= hmercury hoil = (( ? m/? oil ) – 1 ) x ( hHg ) @ 20o C ? m = 13550 Kg /m3 ? oil = 825 Kg /m3 Result Calculation : d = 0. 019 mm A = ( ? d2 /4 ) = 2. 835 x 10-4 m2 ? oil = 825 Kg/m2 ? = 9. 5 x 10-3 pa. s ?mercury = 13550 Kg /m2 L = 4. 014 m Qty Kg Time s Q m3/s x10-4 V m/s h10 cm h18 cm hL Hg cm hL oil m Re 30 107 3. 398 1. 199 11. 2 5. 4 5. 8 0. 895 1978. 35 30 74 4. 914 1. 733 13. 5 5. 5 8 1. 234 2859. 45 30 67 5. 427 1. 914 16. 3 5. 7 10. 6 1. 635 3158. 1 30 51. 22 7. 1 2. 504 18 6. 0 12 1. 851 4131. 6 30 46. 1 7. 888 2. 782 35. 4 7. 3 28. 1 4. 334 4590. 3 30 26. 87 13. 53 4. 772 95. 1 13. 1 82 12. 65 7873. 8 fexp. ftheo. Kind of flow 0. 0144544 0. 00808755 Laminar 0. 00953967 No friction factor Transition 0. 01036214 0. 01057 Turbulent 0. 00685414 0. 00985366 Turbulent 0. 0130014 0. 00959769 Turbulent 0. 01289749 0. 00838651 Turbulent log hL logV log fexp. Log ftheor. log Re -0. 04837 0. 07724 -1. 83698 -2. 09060 3. 29472 0. 09129 0. 23753 -2. 01791 No 3. 45501 0. 21351 0. 27631 -1. 97325 -1. 97582 3. 49380 0. 26738 0. 39791 -2. 16257 -2. 00622 3. 61539 0. 63691 0. 44374 -1. 88471 -2. 01768 3. 66123 1. 10202 0. 67873 -1. 88958 -2. 07643 3. 89621 Sample of calculation : Take first reading : Q = Qty / (? oil x time ) = 3. 398 x10-4 m3/s V = Q/A =1. 199 m/s hL( Hg) = h10 – h18 = 5. 8 cm hL ( oil ) = hL( Hg) ((? Hg / ? oil ) – 1 ) x ( 1 /100 ) = 0. 895 m fexp. = ( hL ( oil ) /V2 ) x ( 0. 0232175) = 0. 0144544 Re = ( ? oil V d / ? ) =1978. 35 2000 Laminar ftheo. = ( 16 / Re ) = 0. 00808755 . Discussion Conclusion : In this experiment we use oil in pipe use mercury in head loss pipes ,why ? Because the head loss when we use mercury larger than oil . So we can take the reading .