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# acoustics Sound Fluids Darcy formula

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• Sound 05/02/2006 Lecture 10
• ### acoustics Sound Fluids Darcy formula

1. 2. FLUID MECHANICS In the built environment pipes are used to convey gas, water and other fluids. In sanitary and drainage works the pressures developed by fluids in motion determine the size and gradients to be employed.
2. 3. To make appropriate and efficient use of fluids it is crucial that we understand their properties and can describe, at least approximately, their behaviour under varying conditions. It is also necessary to control the flow of fluids under these varying conditions and so be able to specify equipment capable of that control. Edexcel Level 5 BTEC HNC in Construction…. Required knowledge
3. 4. Fluids flowing through enclosed pipes behave in several ways; some of these ways are shown here. Regular laminar flow Laminar flow with friction slowing molecules at the pipe walls Turbulent flow Irregular flow across pipe diameter causing increase in velocity
4. 5. Quantity of flow The quantity of fluid flowing past a fixed point can be expressed in terms of:     litres per second or cubic metres per second (cumecs).
5. 6. The quantity of fluid is found by the use of the formula:   Q = AV Where: A is the cross sectional area of the pipe in metres. Q is the quantity of fluid. V is the velocity of the flow.
6. 7. Fluid in pipelines The quantity and velocity of fluid in a pipeline and its relationship with the cross sectional area allows us to calculate and predict the flow of fluid at any point. Using the formula Q = VA If certain information is available we can determine the rate of flow (Q, in cumecs) and the velocity (in metres per sec) and the diameter of the pipe calculated in metres or millimetres.
7. 8. Friction in the pipeline As a fluid flows through a pipeline there is a slowing of the particles closest to the interface between the internal walls and the fluid due to friction . A number of formulae have been developed to quantify and predict the amount of head loss resulting from the friction within a pipeline running full bore. One of the most commonly used formulas is the D'Arcy formula .
8. 9.   h = (4 f L V 2 ) (2g D) D'ARCY formula: ( Write it down ) Where:   h is the head loss over a given length f is the coefficient of friction (fluid to internal surface) Unless there is evidence to the contrary assume 0.0084 V is the velocity of flow in m/sec G is gravitational acceleration assumed to be 9.81 m/sec D is the internal diameter of the pipe in metres.
9. 10. Task:- use the formula to calculate the head loss in a 19 mm diameter cold water supply pipe 8 metres long if the flow is known to be 0.75 m/sec. h = (4 x 0.0084 x 8 x 0.75 2 ) (2 x 9.81 x 0.019)   h = 0.406 metres.
10. 11. Tasks : Calculate the head loss in a 50 mm diameter pipe 25 metres long if the flow is known to be 2.53 m/sec. (5.48 metres) Find the velocity of flow when the head loss is 1.16 metres over a 10 metre length in a 25 mm diameter pipe. (1.3 m/sec) Determine the diameter of a pipe where a head loss of 0.19 metres is experienced over a 16 metre length having a velocity of 0.5 m/sec. (36 mm)