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
where,
= velocity head
= 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.
- Kinetic Energy correction factor
(i) For laminar flow in pipes, a = 2
(ii) For fully develop turbulent flow 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
P_{1}A_{1} – P_{2}A_{2} cos q +
F_{x} = rQ (V_{2} cos q – V_{1})
F_{y} – P_{2}A_{2} sin q = rQ (V_{2} sin q – 0)
F_{x} and F_{y} represents the reaction of bend on water.
- Torque exerted by the water on the pipe will be
T = rQ_{1} V_{1} r_{1} - rQ_{2} V_{2} r_{2}
V_{1} = tangential velocity component of absolute velocity at 1
V_{2} = tangential velocity component of absolute velocity at 2