Basic Equations of Steady Fluid flow

Basic Equations of Steady Fluid flow

(In comparison with those in Dynamics)

Q_in, E_in (or E1)-> | System with energy loss | -> Q_out, E_out (or E₂)
(upsteam) -----------> (down stream)

Hydraulic Head 'E' = Energy/weight = z+p/g +v²/(2g)

Hydraulics Dynamics

Continuity
(chapter 4)
Pg. 116,
Q_in =Q_out
A₁V₁ = A₂V₂
Mass(1) - Mass (2) = 0

Energy Conservation
(Chapter 5,
page 142,
eq 5.13)
1) E_in= E_out + h_L
where h_Lis the head loss

or
2) [ z+p/g +v²/(2g)]_in
= [ z+p/g +v²/(2g)]_out+ h_L
or
3) [ z1+p1/g +v1²/(2g)]
= [ z2+p2/g +v2²/(2g)]+ h_L

Note: E_in = upstream energy
E_out= downstream energy

E_in= E_out + work
Where energy include
P.E.=mgz
and
K.E.=mv² /2

Momentum-Impulse
(chapter 6,
page 189, eq 6.6,
page 190, eq. 6.7)
1) rQ( u₂-u₁) = F
where u1, u2, F are vectors
2) The x, and y components of above equation:

rQ( u_x2-u_x1) = F_x
rQ(u_y2-u_y1) = F_y
m.du/dt =F
(m/dt).du = F
(m/dt)(u2-u1)=F
where: m=r.V
m/dt=r.(~~V/dt~~ ) =rQ

	Hydraulics	Dynamics
Continuity (chapter 4) Pg. 116,	Q_in =Q_out A₁V₁ = A₂V₂	Mass(1) - Mass (2) = 0
Energy Conservation (Chapter 5, page 142, eq 5.13)	1) E_in= E_out + h_L where h_Lis the head loss or 2) [ z+p/g +v²/(2g)]_in = [ z+p/g +v²/(2g)]_out+ h_L or 3) [ z1+p1/g +v1²/(2g)] = [ z2+p2/g +v2²/(2g)]+ h_L Note: E_in = upstream energy E_out= downstream energy	E_in= E_out + work Where energy include P.E.=mgz and K.E.=mv² /2
Momentum-Impulse (chapter 6, page 189, eq 6.6, page 190, eq. 6.7)	1) rQ( u₂-u₁) = F where u1, u2, F are vectors 2) The x, and y components of above equation: rQ( u_x2-u_x1) = F_x rQ(u_y2-u_y1) = F_y	m.du/dt =F (m/dt).du = F (m/dt)(u2-u1)=F where: m=r.V m/dt=r.(~~V/dt~~ ) =rQ