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Hydraulics
| Question | Answer |
|---|---|
| Newtons second law | a=F/m kg(m/s^2) |
| Gamma water | 9810N/m^3 |
| Rho water | 1000kg/m^3 |
| Gamma air | 12 N/m^3 |
| Sg of freash water | 1.0 |
| Sg of sea water | 1.03 |
| Sg of oil | . 80 |
| Sg of Mercury | 13.6 |
| 1 atm | 101.325 KPa |
| Mass density | Rho = M/V |
| Specific valume | Vs=1/rho |
| Unit weight/ specific weight | Gamma=W/V Gamma rho(g) W=mg |
| Specifif gravity | S=rholiquid/rhowater =rhobgas/rho air |
| Unit preasure | P=F/A |
| Absolute pressure | Pabs=Pgage + Patm Pbot=§gammah +Pa |
| Pressure head | h=P/gamma |
| To convert Preasure head | hB= (SgA/SgB) (hA) |
| Capillarity | h =4stresscos0/gammaD |
| Righting moment and overturning moment | RM or OM =BF MGsin0 |
| Metacentric height | MG= MBo+GBo G is below Bo MG= MBo-GBo G is above Bo |
| Rectangular parallelepied | Mbo= B^2/12D (1+.5tan^2 0) |
| Other section | MBo= Vs/VD sin0 MBo= I/VD initial value |
| Weight of dam | W=gammacV |
| Weight of water above dam | Pv= gammav |
| Hydrostatic Uplift | U= gammaVu |
| Total hydrostatic force actingg at vertical projection of submerged portion of dam | Ph= gamma hA |
| Righting moment | RM= W1x1+W2x2 |
| Overturning Moment | OM = Ph+U1z1 |
| Location of Ry | Xbar=RM-OM/Ry |
| FS against overturning | F.O.= RM/OM |
| FS against Sliding | F.S= fiRy/Rx |
| Foundation Pressure e<B/6 | qmin= Ry/B(1-Ge/B) qmax= Ry/B(1+Ge/B) |
| Foundation preassure e>B/6 | qmax= 2Ry/3xbar qmin=0 |
| Circumferential stress in pipes and tanks | Stresst = pD/2t(eff) Eff. If not mentioned assume 100% |
| Hoops carrying stress in pipes and tanks | S=2T/pD T=Stresst A |
| Moving vessel Horizontal Motion | Tan 0= a/g |
| Inclined motion( MV) | Tan 0= ah/g+-av |
| Vertical motion (MV) | P=gammah (1+_a/g) |
| Rotating vessel | Tan 0 = w^2x/g slope of para boloid y= w^2x^2/2g h=w^2r^2/2g |
| Volume of paraboloid | V=1/2 pir^2h |
| Volume flowrate | Q=AV m^3/s |
| Mass Flow Rate | M=rhoQ N/S |
| Weight Flowrate | W=gammaQ kg/s |
| Kinetic energy or velocity Head | v^2/2g |
| Elevation head(potential energy) | Z |
| Total head | v^2/2g + P/gamma + z |
| Power and efficiency | P=QgammaE Eff= (output/input) x100% |
| Energy eq w/o headlost: theoretical | v1^2/2g +P1/gamma +z1 =v2^2/2g +P2/gamma +z2 |
| Bernoullis energy theorem | E1+HA-HE-HL= E2 |
| Energy eq w/ headlost:actual | v1^2/2g +P1/gamma +z1 =v2^2/2g +P2/gamma +z2 +HL |
| Energy Equation w/ pump | E1-HE-HL=E2 (v1^2/2g +P1/gamma +z1+ HA) =(v2^2/2g +P2/gamma +z2) |
| Energy Equation w/ pump( output power of pump) | QgammaHA |
| Energy eq w/ turbine | E1-HE-HL1-2=E2 v1^2/2g +P1/gamma +z1 =v2^2/2g +P2/gamma +z2+HL +HE |
| Energy eq w/ turbine(input power) | QgammaHE |
| Darcy-weisbach formula | hf=fL/D v/2g - allsection hf= 0.0826fL Q^2/D^5- circular pipes |
| Mannings Formula | hf=6.35n^2 L(v^2 /D^4/3) - all section hf= 10.29n^2 (Q^2/D^16/3) - circular pipes |
| HAZEN WILLIAMS | v=0.849CR^0.63 s^0.54 Q=0.2785CD^2.63 s^0.54 - all sections hf=10.64LQ^1.85/C^1.85 D4D^4.87 - circular pipes |
| Slope of the egl, hydraulic slope, energy gradient | S= HL/L =hf/L |
| Specific Energy | H= v^2/2g +d |
| Chezy formula | hL=SL |
| For non circular pipe | R=A/P |
| Minor Losses( due to chage in size direction) | hm=km(v^2/2g) |
| Pipes in Series | Q1=Q2=Q3 HL=hf1+hf2+hf3 hf=deltaP/gamma |
| Pipes in parallel | Q1=Qa+Qb Q2=Qa+Qb hfa=hfb |
| Water hammer | c=square rootof EB/rho for rigid pipes c= square root of Ec/rho 1/Ec=1/EB+d/Et c=square root of EB/rho(1+EBd/Et) |
| Rapid closure (tc<2/Lc) | Phj rhocv |
| Slow closure (tc>2Lc) | Phprime= 2Lrhov/tc |
| Reynold number | NR =vD/v v=fi/rho |
| If NR<2000 | f=64/NR |
| If NR> 2000 | 1/square root of f =log( strain/ 3.7D + 2.51/NR square root of f) |
| Open channel | Q=AV |
| v by chezy | V=Csqr. RS |
| Hydraulict Radius | R= A/P |
| Chezy coefficient | m^1/2/s c=sqr. 8g/f |
| C by manning | C=1/n R^1/6 |
| C by bazin | C= 87/1+m/sqr.R |
| C by kutter | C= [ (1/n)+23 + (0.00155/s)]/[1+ n/sqr. R(23 +0.00155/s) |
| Chezy manning formula | V= 1/n R^2/3 s1/2 |
| Impact of jet on plane | F=rhoQv |
| Force on pipes bend anf roducer | §Fx =rhoQ(V2x-V1x) §Fy=rho(V2y-Viy) F=¶Fx^2+Fy^2 |
| Force on curved vane | §Fx=rhoQ(v2x-v1x) §Fy=rhoQ(v2ygv1y) |
Created by:
Joshua Gabriel