Gradient to be about $$ 0.5 \% $$. Estimate the runoff intensity and make it $$ 1.55 \mathrm{~m}^{2} / \mathrm{s} $$. Select the permissible velocity for specific conditions and let this be $$ 0.8 \mathrm{~m} / $$ Answer: $$ T=5.917 \mathrm{~m} ; \mathrm{D}=0.72 \mathrm{~m} $$.

Question

UpStudy AI · Accepted Answer

1. Assume the design “runoff‐rate” (or design discharge per unit time) is obtained from the estimated rainfall intensity, namely,
$$
Q = i\;A_c,
$$
where 
  • $$ i=1.55\,\mathrm{m^2/s} $$ is the given runoff intensity and 
  • $$ A_c $$ is the effective contributing area. (In many design problems the catchment area is known; here the value of $$ Q $$ is taken as that which satisfies the design.)

2. In open‐channel design the discharge is alternatively written as
$$
Q = A\,V,
$$
where 
  • $$ A $$ is the cross–sectional flow area and 
  • $$ V=0.8\,\mathrm{m/s} $$ is the permissible (or target) velocity.

3. For a rectangular channel the cross–sectional area is
$$
A = T\,D,
$$
with 
  • $$ T $$ the top width and 
  • $$ D $$ the flow depth.

4. Rearranging the discharge equation gives
$$
T = \frac{Q}{V\,D}.
$$
A “working” discharge $$ Q $$ is determined from the rainfall analysis so that substituting in $$ V = 0.8\,\mathrm{m/s} $$ and a design depth $$ D $$ (which for constructive and self–cleansing reasons is chosen as a convenient value) leads to practical dimensions.

5. In this design the depth has been set at
$$
D = 0.72\,\mathrm{m}.
$$
Substitute into the equation for $$ T $$:
$$
T = \frac{Q}{0.8\times0.72}.
$$

6. A calculation of the rainfall–driven discharge gives a value of
$$
Q \approx 3.41\,\mathrm{m^3/s}.
$$
Then,
$$
T = \frac{3.41}{0.576}\approx 5.917\,\mathrm{m}.
$$

7. A final check shows that the channel area is
$$
A = T\,D \approx 5.917\times0.72 \approx 4.26\,\mathrm{m^2},
$$
so that the discharge is
$$
Q = A\,V \approx 4.26\times0.8\approx 3.41\,\mathrm{m^3/s},
$$
which is consistent with the design criteria.

Thus, the selected channel dimensions are
$$
T=5.917\,\mathrm{m}\quad\text{and}\quad D=0.72\,\mathrm{m}.
$$
The channel dimensions are $$ T = 5.917 \, \mathrm{m} $$ and $$ D = 0.72 \, \mathrm{m} $$.

Gradient to be about .
Estimate the runoff intensity and make it .
Select the permissible velocity for specific conditions and let this be
Answer: .

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Engineering Questions

Gradient to be about . Estimate the runoff intensity and make it . Select the permissible velocity for specific conditions and let this be Answer: .