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<br />t.
<br />.,
<br />
<br />.
<br />
<br />.....
<br />
<br />120
<br />
<br />HYDRAULIC ENGINEERING ''/4
<br />
<br />where. = specific gravily of the sedimenl. The values of I" calculaled from lhe field
<br />data arc plOlled againsl t."" in Fig 2. Despile the wide scalier (r' = 0.3882) a
<br />functional relation betweenf" and 1'.0,0 is evident which indicates thatf- decreases
<br />with increasing bed mobilily. This result is conslslenl with previous work. Assuming
<br />a wide channel approximation the value (tDill can be expressed as:
<br />f'
<br />T" --'T' (9)
<br />D. - /' + f~ D.
<br />
<br />where " "" is calculaled with the IOtaI shear stresS.
<br />
<br />In Fig 3(a) and (b) the data is subdivided such Ihal I U is plotled against the IOlaI
<br />dimcnsionless shear suess """ ia (a), and agaiasl I '/if' + I U) in (b). The
<br />relationship between I" and "0.. appears IOtally random. II is evidenl Ihal any
<br />functional relation hetween I" and t."" is due 10 the relationship helweenl" and
<br />I'/if' + 1"). Since the variation in I' is small compared to 1", I'/if' + 1") can lie
<br />approximaled by a/(a + I") where a is equal to the mean value of I' from the data
<br />set The value uf ,. obtained from a regression helweea I'/if' + 1") and a/(a + 1")
<br />with a = 0.048 is 0.9573. This indicales thai 95% of the observed variation helween
<br />/ H and 1'- Dso is due to spurious correlation. It must therefore be concluded the
<br />empirical bar resistanCe curves of Einslein and Barbarossa (1952) and Parker and
<br />Pelerson (1980) largely resull from spurious correlation, and do nol give any
<br />meaningful predictions of the fonn or bar rouglmess.
<br />
<br />Concl....ons
<br />Evea at high in.bank nows the fonn roughness can he significanl. or even much
<br />grealer than the grain roughness in gravel rivers. While the value of I' can he readily
<br />calculaled from Ihe observed hydraulic geometry, no method is yel available 10
<br />reliably eslimale f". Empirical heal-fit equations which do nol distinguish belweea
<br />grain and bar roughness such as Hey (1979), Bray (1979), and Eqn (1) wilh k, = 7.0
<br />D", herein, arc associated with such a large degree of scalier Ihal their practical use
<br />islimi1.ed.
<br />
<br />Aa area for fUlure investigation is to delennine the facturs thai innuence I". A
<br />program involving detailed description of the channel geometry adjacenl 10 gauging
<br />Slalions would be a first step to recognizing ia Ihe field lhe channel fealures lhal
<br />contribUIe to the fonn roughness. For instance PreSlegaard (1983) has had some
<br />success in relating the fonn roughness 10 the magnitude of the hars. This work could
<br />produce guidelines for hetler estimation of r.
<br />
<br />ReFerences
<br />Aadrews, E.O., 1984: "Bed malerial enlrainmenl and the hydraulic geometry of
<br />gravel- hed rivers ia Colorado." Oeol. Soc. Am. Bull., 95, 371-378.
<br />Bazin, H.E.. 1865: "Recherches hydrauliques. memoires presentes par divers
<br />savants, science, mathematiques tl physiques." Series 2, 19. Paris, France.
<br />
<br />.
<br />
<br />FLOW RESlSTANCE-(]RAVEL CHANNELS
<br />
<br />.
<br />
<br />121
<br />
<br />Bray, 0.1.,1979: "Estimating average velocily in gravel-bed rivers." J. Hydr. Div..
<br />ASCE, 105 (9),1103-1122.
<br />Charllon, F.G., Brown, P.M., and Benson, R.W., 1978: "The hydraulic geomelry of
<br />some gravel rivers in Britian." Rept. IT 180, Hydr. Res. SID.. Wallingford,
<br />UK, 48 p.
<br />Einslein, H.A., and Barbarossa, N_, 1952: "River channel roughness." Tr/JIIS. ASCE,
<br />117, Pap. No. 2528, 1121-1146.
<br />Hey, R.D., and lhome, C.R., 1986: "S18ble channels with mobile gravel beds." J.
<br />Hydr. Div.. ASCE, 112, (8), 671-689.
<br />Keulegan, G.H., 1938: "Laws oflurbulenl now in open channels." J.Nat. Bur_
<br />Stand.. 21, Res. Pap.. 1151,707-741.
<br />Parker, G.. and Pelerson, A.W., 1980: "Bar resistance of gravel bed rivers." J. Hydr.
<br />Div.. ASCE, 106 (10), 1559-1575.
<br />Preslegnard, K.L., 1983: "Bar resistance in gravel hed streams al bankfull stage."
<br />War. Res. R."., 19(2), 472.476.
<br />Vanoni, V.A., 1975: Sedimentation engineering. A.S.C.E. Manuals and Repons on
<br />Engineering Practice, 54, 745p.
<br />
<br />0.7
<br />0..
<br />O.S
<br />.... 0..
<br />0.3 .0
<br />0..
<br />0.1
<br />
<br />...00
<br />
<br />0..
<br />
<br />......c,.- 7.0
<br />.
<br />-c,.-1.0
<br />
<br />.....f.
<br />"=-0.3881
<br />
<br />0..
<br />
<br />".
<br />
<br />.... 0..
<br />
<br />( D
<br />
<br />.~"O OI,/lo a
<br />0.2 :",66:.M:~
<br />dP"1' PIA. ~
<br />03 5 10 20 30 50 100
<br />
<br />
<br />0.04 0.08
<br />T"
<br />D"
<br />
<br />YID..
<br />
<br />Figure I. Variation of lwith YID",.
<br />
<br />Figure 2. Relationship between
<br />I" and t."".
<br />
<br />(a) 0.7
<br />0..
<br />o.s
<br />',- 0.4
<br />0.3
<br />0.'
<br />0.1
<br />
<br />00
<br />
<br />(b) 0.7
<br />0.6
<br />o.s
<br />'- 0.4
<br />0.3
<br />D.2
<br />0.1
<br />
<br />00
<br />
<br />0.2 0.4 0.6 0.8
<br />
<br />e/(e+n
<br />,e=D.fU73
<br />
<br />00..
<br />.
<br />r.
<br />, ~ '0"-: 0 o. II
<br />" .... 0 D,;
<br />. ., to. oil..
<br />
<br />
<br />0.04
<br />
<br />0.08 0.12 0.18
<br />T .
<br />D"
<br />
<br />Figure 3. Variation ofl" with (a) ,'0... (b) I'/(f' +1").
<br />
<br />f'I(f' + f")
<br />
<br />-
<br />
<br />..
<br />
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