Responde Aí
Acesse com GoogleAcesse com AppleAcesse com Facebook

Enunciado

FenTrans, MecFlu, TransCal e TransMassa - Frank White - Mecânica dos Fluidos- Ed: 8º - Capítulo 10.Problemas - Ex. 19

Modify Prob. P10.18, the 908 V channel, to let the surface

be clean earth, which erodes if the average velocity exceeds 6 ft/s. Find the maximum depth that avoids erosion.

The slope is still 3 m per km.

Passo 1

Saaaalve, tranquilo? Vamos lá resolver mais uma questão juntos?! 😊

Considere o canal de aço pintado em forma de V com um ângulo de 90 °

Passo 2

Calcule a área do canal:

A = y 2 c o t ⁡ θ

Onde, y é a profundidade do canal e θ é o ângulo

A   = y 2 c o t ⁡ 45 ∘   = y 2

Calcule o perímetro molhado:

P   = 2 b   = 2 y c o s ⁡ 45 ∘   = 2 2 y

Passo 3

Calcular o raio hidráulico:

R h = A P

Substituindo valores

R h   = A P   = y 2 2 2 y   = y 2 2

Passo 4

Declive

S 0   = 3 1000   = 0.003

Para a terra limpa, o fator de Manning n é 0.022 ,Calcule a velocidade média:

V   = 6 f t / s   = 6 f t s × 0.3048   m 1 f t   = 1.83   m / s

Assim, a velocidade é dada como,

V = 1 n R h 2 / 3 S 0 1 / 2

Substituindo valores

V   = 1 n R h 2 / 3 S 0 1 / 2 1.83   = y 2 / 3 × 0.003 1 / 2 ( 2 2 ) 2 / 3 0.022 y   = 1.83 × 0.022 ( 2 2 ) 2 / 3 0.003 1 / 2 3 / 2   = 1.78   m

Portanto, a profundidade máxima que evita a erosão é 1.78   m .

Resposta

y = 1.78   m

Exercícios de Livros Relacionados

An engineer makes careful measurements with a weir (seeSec. 10.7) that monitors a rectangular unfinished concretechannel laid on a slope of 18. She fi nds, perhaps with surprise, that when the water d
A trapezoidal channel has n 5 0.022 and S0 5 0.0003 andis made in the shape of a half-hexagon for maximumefficiency. What should the length of the side of the hexagon be if the channel is to carry 225
What are the most effi cient dimensions for a half-hexagoncast iron channel to carry 15,000 gal/min on a slopeof 0.168?
A rectangular channel, laid out on a 0.58 slope, delivers aflow rate of 5000 gal/min in uniform fl ow when the depthis 1 ft and the width is 3 ft. (a) Estimate the value ofManning’s factor n. (b) What
A V-shaped painted steel channel, similar to Fig. E10.6,has an included angle of 908. If the slope, in uniform flow,is 3 m per km, estimate (a) the fl ow rate, in m3/s and (b) theaverage wall shear st