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Note for Fluid Mechanics and Hydraulic Machines - FMHM By JNTU Heroes

  • Fluid Mechanics and Hydraulic Machines - FMHM
  • Note
  • Jawaharlal Nehru Technological University Anantapur (JNTU) College of Engineering (CEP), Pulivendula, Pulivendula, Andhra Pradesh, India - JNTUACEP
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CIVE1400: Fluid Mechanics Section 1: Fluid Properties We know that fluids flow under the action of a force, and the solids don’t but solids do deform. CIVE1400: Fluid Mechanics What use can we make of these ideas? In the analysis of fluids we often take small volumes (elements) and examine the forces on these. So we can say that xfluids lack the ability of solids to resist deformation. Take the rectangular element below. xfluids change shape as long as a force acts. smartworlD.asia What forces cause it to deform? (These definitions include both gasses and liquids as fluids.) A C CIVE1400: Fluid Mechanics Section 1: Fluid Properties Section 1: Fluid Properties 3 CIVE1400: Fluid Mechanics B D Section 1: Fluid Properties 4

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CIVE1400: Fluid Mechanics Section 1: Fluid Properties A’ B’ F CIVE1400: Fluid Mechanics Section 1: Fluid Properties Fluids in motion Consider a fluid flowing near a wall. - in a pipe for example - F C D Fluid next to the wall will have zero velocity. Forces acting along edges (faces), such as F, are know as shearing forces. The fluid “sticks” to the wall. From this we arrive at the definition: Moving away from the wall velocity increases to a maximum. smartworlD.asia A Fluid is a substance which deforms continuously, or flows, when subjected to shearing forces. This has the following implications for fluids at rest: v Plotting the velocity across the section gives “velocity profile” If a fluid is at rest there are NO shearing forces acting on it, and any force must be acting perpendicular to the fluid Change in velocity with distance is “velocity gradient” = CIVE1400: Fluid Mechanics Section 1: Fluid Properties 5 CIVE1400: Fluid Mechanics du dy Section 1: Fluid Properties 6

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CIVE1400: Fluid Mechanics Section 1: Fluid Properties As fluids are usually near surfaces there is usually a velocity gradient. CIVE1400: Fluid Mechanics Section 1: Fluid Properties What use is this observation? Under normal conditions one fluid particle has a velocity different to its neighbour. Particles next to each other with different velocities exert forces on each other (due to intermolecular action ) …… It would be useful if we could quantify this shearing force. This may give us an understanding of what parameters govern the forces different fluid exert on flow. smartworlD.asia i.e. shear forces exist in a fluid moving close to a wall. We will examine the force required to deform an element. What if not near a wall? Consider this 3-d rectangular element, under the action of the force F. v No velocity gradient, no shear forces. CIVE1400: Fluid Mechanics Section 1: Fluid Properties 7 CIVE1400: Fluid Mechanics Section 1: Fluid Properties 8

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CIVE1400: Fluid Mechanics Section 1: Fluid Properties CIVE1400: Fluid Mechanics δx A 2-d view may be clearer… b a δz Section 1: Fluid Properties A’ B F E x φ B A B’ F E’ y δy F C F D The shearing force acts on the area C A Gz u Gx D under the action of the force F Shear stress, W is the force per unit area: a a’ smartworlD.asia b W b’ F A A’ B The deformation which shear stress causes is measured by the angle I, and is know as shear strain. B’ E F C F A Using these definitions we can amend our definition of a fluid: D In a fluid I increases for as long as W is applied the fluid flows In a solid shear strain, I, is constant for a fixed shear stress W. CIVE1400: Fluid Mechanics Section 1: Fluid Properties 9 CIVE1400: Fluid Mechanics Section 1: Fluid Properties 10

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