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**Chapter 5 Fluid Dynamics**

- Reynolds equation = Intertia force + gravity force + viscous force + turbulence force + pressure force
- Navier - Stoke's equation = Intertia gravity force + pressure force + viscous force
- Eulers equation (represents momentum equation in a 2-D, inviscid steady flow) Inertia force = gravity force + pressure force
- Bernoulli's equation (Conservation of Energy) Assumptions in Bernoullis equations:

(i) fluid is ideal

(ii) flow is steady

(iii) flow is continous

(iv) fluid is incompressible

(v) flow is non-viscous

(vi) flow is irrotational

(vii) applicable along a stream line Z cons tant pg P

where,

= velocity head

p/rg = pressure head

z = elevation of datum head

= piezometric head

- The line representing the sum of all 3 heads is known as total energy line or total head line.
- Line joining the points of piezometric heads is known as hydraulic grade line or piezometric line.
- Piezometric head remains constant normal to the stream lines in case of uniform diameter straight pipe.
- Flow in pipe bend, considered as irrotational flow. Piezometric head line for outer boundary is above than the inner boundary and pressure is also more at outer boundary
- HGL is always parallel and lower than TEL.
**Energy gradient**

**Hydraulic gradient**

**Kinetic Energy correction factor**(i) For laminar flow in pipes, a = 2 (ii) For f ully devel op turbulent f low in pipes, a = 1.33 Lower value is applicable for rough surface and high Reynolds number. **Pressure at**stagnation point where velocity of flow is zero is known as the stagnation pressure.

where p_{o} = static pressure and

= dynamic pressure

**Flow through Pipe bend**

Fx and Fy represents the reaction of bend on water.

Torque exerted by the water on the pipe will be

V_{1} = tangential velocity component of absolute velocity at 1

V_{2} = tangential velocity component of absolute velocity at 2

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