Solution Manual For Open Channel Hydraulics Sturm 2nd Edition
Solution Manual For Open Channel Hydraulics Sturm 2nd Edition
Solution Manual For Open Channel Hydraulics Sturm 2nd Edition
2
Sturm, T.W., Open Channel Hydraulics, 2nd Edition CHAPTER 1
1.4. The river flow at an upstream gauging station is measured to be 1500 m3/s, and at another
gauging station 3 km downstream, the discharge is measured to be 750 m3/s at the same instant of
time. If the river channel is uniform with a width of 300 m, estimate the rate of change in the
water surface elevation in meters per hour. Is it rising or falling?
Solution.
A y Q 750 −1500
=B =− − = 0.25 m 2 /s
t t x 3000
y 0.25 0.25
= = = 8.33 10 −4 m/s or 3.0 m/hr (rising)
t B 300
1.5. A paved parking lot section has a uniform slope over a length of 100 m (in the flow direction) from
the point of a drainage area divide to the inlet grate, which extends across the lot width of 30 m.
Rainfall is occurring at a uniform intensity of 10 cm/hr. If the detention storage on the paved
section is increasing at the rate of 60 m3/hr, what is the runoff rate into the inlet grate?
Solution.
Utilize the continuity equation for a finite control volume given by Equation 1.3 for an
incompressible fluid so that the fluid density cancels on both sides of the equation. Then we
have
d
= − Q + Q
out in
dt
10
60 = − Qrunoff + 100 30
100cm/m
1.6. If the lake level upstream of the spillway in Figure 1.1c is 55 m above the channel floor at the base
of the spillway just upstream of the hydraulic jump, estimate the depth and velocity there for a
flow rate of 1,000 m3/s and a spillway width of 30 m. What is the value of the Froude number?
Neglect the approach velocity in the lake and the head losses on the spillway.
Solution.
Writing the energy equation from the water surface upstream of the spillway where the velocity
head is negligible to the floor of the stilling basin downstream of the spillway, and neglecting
head losses, we have
3
Sturm, T.W., Open Channel Hydraulics, 2nd Edition CHAPTER 1
q2
y1 = y 2 +
2gy 22
(1000 / 30) 2 56.63
55 = y 2 + = y2 + y 2
19.62 y 22 2
Solving by trial and error for the supercritical solution (see Chapter 2), the result is y2 = 1.024 m
and V2 = q/y2 = 33.33/1.024 = 32.55 m/s. The Froude number becomes
V2 32.55
F= = = 10.3
gy2 9.811.024
which is supercritical and will provide a strong, stable hydraulic jump as shown in Chapter 3.
1.7. A rectangular channel 6 m wide with a depth of flow of 3 m has a mean velocity of 1.5 m/s. The
channel undergoes a smooth, gradual contraction to a width of 4.5 m.
(a) Calculate the depth and velocity in the contracted section.
(b) Calculate the net fluid force on the walls and floor of the contraction in the flow direction.
In each case, identify any assumptions that you make.
Solution.
1
F 2
6m 4.5 m
(a) Apply the energy equation from the approach section 1 to the contracted section 2 with
negligible head losses and assuming a horizontal channel bottom:
V1 2 q2
y1 + = y2 + 2 2
2g 2gy 2
where q2 = V2y2 = (6/4.5)q1 = (6/4.5)(1.5)(3.0) = 6.0 m2/s. Substituting and solving, we have
1.5 2 6.0 2
3.0 + = y2 +
19.62 19.62 y 22
1.835
y2 + = 3.115
y 22
from which y2 = 2.90 m by trial and error and V2 = q2/y2 = 6.0/2.90 = 2.07 m/s. Note that there
are two solutions, but this is the subcritical solution and the correct one as discussed in more
detail in Chapter 2.
4
Sturm, T.W., Open Channel Hydraulics, 2nd Edition CHAPTER 1
(b) Apply the momentum equation in the flow direction in which F = the resultant force of the
walls and floor on the flow. Assume a hydrostatic pressure distribution at sections 1 and 2.
Because the transition is horizontal, there is no component of the gravity force in the flow
direction. The momentum equation becomes
2
y2
− F + b1 y1 − b2 2 = Q(V2 − V1 )
2 2
3.02 2.902
− F + 6.0 9810 − 4.5 9810 = 1000 (1.5 3.0 6.0) (2.07 −1.5)
2 2
1.8. A bridge has cylindrical piers 1 m in diameter and spaced 15 m apart. Downstream of the bridge
where the flow disturbance from the piers is no longer present, the flow depth is 2.9 m and the
mean velocity is 2.5 m/s.
(a) Calculate the depth of flow upstream of the bridge assuming that the pier coefficient of
drag is 1.2.
(b) Determine the head loss caused by the piers.
Solution.
In part (a), apply the momentum equation with the control volume boundaries halfway between
the piers; then apply the energy equation in part (b).
s = 15 m
D
Fp1 Fp2
1 2
y12 y 22 V12
s − s − C A = Q(V −V )
D f 2 1
2 2 2
in which D = drag force on the pier; Fp = hydrostatic force; Af = frontal area of the pier at section
1 on a plane perpendicular to the flow direction = ay1; a = pier diameter = 1.0 m; s = pier spacing
= 15.0 m; CD = drag coefficient =1.2; and Q = A2V2 = (15)(2.9)(2.5) = 108.8 m3/s . Using
continuity and substituting, we have
5
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Language: Italian
IL RICHIAMO
DELLA FORESTA
ROMANZO
PREFAZIONE E TRADUZIONE DI
GIAN DÀULI
MCMXXIV
MODERNISSIMA
MILANO
PROPRIETÀ LETTERARIA RISERVATA
Stab. Tipo-Lit. FED. SACCHETTI & C. — Via Zecca
Vecchia, 7 — Milano
INDICE
JACK LONDON
Credo che non vi sia scrittore il quale abbia vissuto e sofferto, amato
e odiato con tanta disperata e selvaggia intensità, come Jack
London. I Gorki, i Dostoiewski, gli Upton Sinclair, i Rimbaud, i
Baudelaire, tra miserie fisiche e morali, hanno saputo, sì,
rappresentare visioni mai concepite da altri, ma vivendo una vita
che, per quanto agitata, non soffrì che in parte del grandioso e
avventuroso travaglio che agitò l’esistenza dura ed eroica del grande
scrittore americano, le cui opere suscitano in noi sentimenti di paura
e di tenerezza, di amore e di dolore e, soprattutto, di ammirazione.
Ci pare di trovarci di fronte all’uomo delle caverne che riveli alla
nostra sensibilità moderna i misteri e le ferree leggi della vita
primitiva.
Perciò, con senso di pena, ho visto in questi giorni pubblicata, a cura
del Prezzolini, la prima traduzione italiana di uno dei romanzi di Jack
London, «Il lupo di mare», come uno dei tanti libri per ragazzi. Poveri
innocenti! Le opere di London affidate nelle mani di adolescenti che
s’affacciano alla vita, e non conoscono ancora il male, e ignorano i
feroci egoismi degli uomini, la cecità del Dio cristiano, le leggi
inesorabili della natura? Quale errore!
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