Hydraulics

Front 1

Unit weight (gamma)=Weight of fluid over Volume or W over V.

mass density (rho) = M over V, or mass if fluid over volume,.

specific volume = 1 over p (rho),.

pressure disturbances;

celerity= square root of Eb over p,.

Eb is equal to bulk mudulus of elasticity,

unit pressure:,

P= F over A, or force over area,.

atmospheric pressure:

Pressure atmospheric = 14.7 psi, 762mm Hg,101.3 kpa,.

Pressure absolute = Pressure gage + P atmospheric,.

P= unit weight times height of gage)

h= P over gamma h,.

hydrostatic force:,

plane surface= unit weight times h, (is center of gravity) times area,.

Back 1

stress on pipe walls:

tangential stress (St)= pD over 2T,.

longitudinal stress (SL)= pd over 4T,.

wall stress (S) = pd over 4T,.

spacing of hoops (S)= 2 ST times Ah over pD,.

dams:

solving dam probles,

1. consider 1 unit or 1 meter length of dam,

2. determine all the forces acting,

•verical forces;

•weight of the dam,w1=unit weight times v1,w2= unit weight times v2 and w3= unit weight times v3,.

•also weight of water= unit weight times v4,.

force (F) = unit weight times height times Area,.

•hydrostatic uplift, U1 = unit weight time V ,u1, U2= unit weight times V ,u2, U3= unit weight times V3,.

•horizontal forces :

F = Unit weight times h times A,.

• reaction:

vertical reaction,summation forces vertical,Ry = summation forces vertical,.

Ry= W1 + W2 + W3 + W4 minus U1 minus U2,.

Rx= summation forces at horizontal,

Rx=P,.

4. moment about the toe,

Righting moment, (RM) rotation toward the upstream,

RM = W1 times X1,plus w2 times X2 plus w3 times x3 plus w4 times x4,.

OM= Py plus U1Z1 plus U2 Z2,.

5. location of Ry (x),

x= RM minus OM over RY,

factor of safety (against sliding) = u Ry over Rx (greater than 1),.

factor of safety OM,

FSo = RM over Om (greater than 1),.

foundation pressure:

for e less than B over 6:,

q= - Ry over B times (1 plus minus 6e over B ),

for e greater than B over 6:,

q= 2 Ry over 3x,

Front 2

Front (Term)

Back 2

Back (Definition)

Front 3

Bouyancy:,

BF = Wo

BF= Unit weight times volume displaced,

WB = Unit weight times VB,.

Volume displaced over V body = S body over S liquid,.

floating bodies:,

metacentric height (MG) = M Bo plus minus G BO,

use negative if G is above BO,posive if G is below BO,.

Back 3

Relative equilibrium of liquids:, tan theta= a over g,

inclined motion;

tan theta= a x over g plus minus ay,.

positive if upward acceleration,

negative if downward acceleration,

vertical motion:,

P = unit weight h times ( 1 plus a over g),

rotation:

tan theta= w squared x over 2 g,

y = w squared x squared over 2 g,

equation of paraboloid;,

h= w squared r squared over 2 g,

squared property of parabola:

X1 over y1 = X2 over y2,

volume of paraboloid:,

V = one half pie r squared h,.

discharge or flow rate,Q,

Q=AV , V= Q over A,

kinetic head or velocity head:

KE over W = V squared over 2g,.

pressure head= P over unit weight,

E= V squared over 2g Plus P over unit weight plus z,.

power, P = Q unit weight E,

1hp= 746 watts,.

bernoullis energy theorem:,

E1=E2

V1 squared over 2g + P1 over uniy weight +Z1 = V2 squared over 2g + P2 over unit weight + Z2 + HL1-2,

with pump:,

V1 squared over 2g + P1 over uniy weight +Z1+ HA = V2 squared over 2g + P2 over unit weight + Z2 + HL1-2,

pump power= Q times y times HA,

with turbine:

V1 squared over 2g + P1 over uniy weight +Z1 = V2 squared over 2g + P2 over unit weight + Z2 +HE+ HL1-2.,

turbine power= Q y times HE (input power)

efficiency= power output over power input times 100%,.

energy & hydraulic gradeline;:,

hgl= P over y + Z,

energy gradeline (Egl)= V squared over 2g + P1 over unit weight + Z,.