Lecture material on Fluid mechanics II CVE 313pptx

Lecture material

1. CVE 305

2. FLOW THROUGH PIPES

3. INTRODUCTION A pipe is a closed conduit (generally of circular section) which is used for carrying fluids under pressure. The flow in a pipe is termed pipe flow only when the fluid completely fills the cross-section and there is no free surface of fluid. The pipe running partially full (in such a case atmospheric pressure exists inside the pipe) behaves like an open channel.

4. Loss of energy (or Head) in pipes When water flows in a pipe, it experiences some resistance to its motion, due to which its velocity and ultimately the head of water available is reduced. This loss of energy (or head) is classified as follows: A. Major Energy Losses This loss is due to friction. B. Minor Energy Losses These losses are due to : 1. Sudden enlargement of pipe, 2. Sudden contraction of pipe, 3. Bend of pipe, 4. An obstruction in pipe, 5. Pipe fittings, etc.

5. FLOW THROUGH PIPES ENERGY LOSSES These losses which are due to friction are calculated by : Darcy- Weisbach formula 2. Chezy’s formula.

6. Darcy- Weisbach Formula The loss of head (or energy) in pipes due to friction is calculated from Darcy- Weisbach formula which is given by: The head loss due to friction is ( Hf ) = (4ƒ * L P /D P ) (V 2 /2g) Where L P = Total length of pipe D P = Diameter of pipe ƒ = 64/Re = Frictional factor which depends on the value of Reynolds number (Re).

7. Reynolds number (Re) = (VD P )/ Ѵ Where V = mean velocity of flow D P = diameter of pipe Ѵ = Kinematic viscosity V 2 /2g = Velocity head Darcy- Weisbach Formula cont. ƒ = coefficient of friction (a function of Re no.) ƒ = (0.0791)/(Re) 1/4 for Re varying from 4000 to 10 6 ƒ = 16/Re for Re < 2000 (laminar/viscous flow)

8. Losses in pipe Cont. Chezy ’s formula for loss of Head due to friction An equilibrium between the propelling force due to pressure difference and the frictional resistance gives: (p 1 -p 2 )A= ƒ’PLV 2 o r .A = ( ƒ’/w)PLV 2 or h f = ( ƒ’/ w )(P/A)PLV 2 Therefore Mean velocity, V = *  

9. Where, the factor , is called the Chezy’s constant, C ; The ratio A/P {= area of flow/wetted perimeter) is called the hydraulic mean depth or hydraulic radius and denoted by m (or R ) the ratio prescribes the loss of head per unit length of pipe and is denoted by i or s (slope). Therefore Mean Velocity, V = C this equation is known as Chezy’s formula.  

10. This formula ( V = C ) helps to find the head loss due to friction if the mean flow velocity through the pipe and also the value of Chezy’s constant C are known . Note: ( i ) Darcy- Weisbach formula (for loss of head) is generally used for the flow through pipes. ( ii ) Chezy’s formula (for loss of head) is generally used for the flow through open channels. ( iii ) The values of hydraulic mean depth for a circular pipe , m = D/4 therefore m = area/perimeter = ( π D 2 /4)/ π D = D/4  

11. Example 1. In a pipe of diameter 350 mm and length 75 m water is flowing at a velocity of 2·8 m/s. Find the head lost due to friction using : Darcy- Weisbach formula ; ( ii ) Chezy’s formula for which C = 55 . Assume kinematic viscosity of water as 0·012 stoke.

12. Example 2 . Water flows through a pipe of diameter 300 mm with a velocity of 5 m/s. If the co-efficient of friction is given by f = 0.015 + (0.08/Re 0.3 ), where Re is the Reynolds number . Find the head lost due to friction for a length of 10 m. Take kinematic viscosity of water as 0·01 stoke.

13. Example 3. In a pipe of 300mm diameter and 800m length an oil of specific gravity 0.8 is flowing at the rate of 0.45m 3 /s. Find: Head lost due to friction and Power required to maintain the flow. Take kinematic viscosity of oil as 0.3 stroke = 0.3x10 -4 m 2 /s

14. Example 4 . Water is to be supplied to the inhabitants of a college campus through a supply main . The following data is given : Distance of the reservoir from the campus = 3000 m Number of inhabitants = 4000 Consumption of water per day of each inhabitant = 180 litres Loss of head due to friction = 18 m Co-efficient of friction for the pipe, f = 0·007 If the half of the daily supply is pumped in 8 hours, determine the size of the supply main.

15. Exercise. A pump delivers water from a tank A (water surface elevation = 110m) to tank B (water surface elevation = 170m). The suction pipe is 45m long (frictional factor, f = 0.024) and 35cm in diameter. The delivery pipe is 950m long (f= 0.022) and 25cm in diameter. The head discharge relationship for the pump is given by Hp = (90-800Q2), where Hp is in meters and Q in m3/s. Calculate: The discharge in the pipeline The power delivered by the pump .

16. MINOR ENERGY LOSSES Whereas the major loss of energy or head is due to friction, the minor loss of energy (or head) includes the following cases: Loss of head due to sudden enlargement, Loss of head due to sudden contraction, Loss of head due to an obstruction in the pipe, Loss of head at the entrance to a pipe, Loss of head at the exit of a pipe , Loss of head due to bend in the pipe, and Loss of head in various pipe fittings