- 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
= 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 po = static pressure and
= dynamic pressure
P1A1 – P2A2 cos q +
Fx = rQ (V2 cos q – V1)
Fy – P2A2 sin q = rQ (V2 sin q – 0)
Fx and Fy represents the reaction of bend on water.
- Torque exerted by the water on the pipe will be
T = rQ1 V1 r1 - rQ2 V2 r2
V1 = tangential velocity component of absolute velocity at 1
V2 = tangential velocity component of absolute velocity at 2