Following are the results obtained in the Below steps;
Flow type: Sub-critical (Fr < 1)
Momentum function value: 0
Conjugate depth: 0.7 m, 0.3 m
Alternate depth: 0.98 m
Minimum specific energy: 0.53 m
Critical depth: 0.67 m
Minimum Momentum function: 0.81 m
If there's a jump formed at 1 m depth;
Starting depth of jump = d = 1.0 m
Finishing depth of jump = 0.7 m
Jump height = 0.3 m
Energy loss due to jump = 0.81 m
Length of jump = 0.81 m.
Explanation:
Given data;
Bottom width (b) = 2.0 m
Flow rate (Q) = 4.0 m³/s
Flow depth (d) = 1.0 m
Step 1: Froude number calculation;
Fr = V/√gd
Where V = Q/A
= Q/bd; here, A = bd
√gd Fr = Q/bd /
Fr = Q/ √gbd³
Fr = 4.0 / √(9.81 x 2.0 x 1.0³)
Fr = 0.90 < 1
Flow type is sub-critical.
Step 2: Momentum function calculation;
M = (Q/2g) (d²/dy²) [(y + d)²/4]
M = (4.0/2x9.81) (0) [(1 + 1)²/4]
M = 0
The momentum function value is zero.
Step 3: Conjugate depth calculation;
d1 + d2 = 2d;
d1d2 = Q² / (gbd³)
Let's take d1 as 0.7 m and calculate d2.
d1 + d2 = 2d
d2 = 2d - d1
d1d2 = Q² / (gbd³)
d2 = (Q² / (gbd³) ) / d1
d2 = (4.0² / (9.81 x 2.0 x 1.0³)) / 0.7
d2 = 0.3 m
Check: d1 + d2 = 0.7 + 0.3 = 1.0 m which is equal to the flow depth.
Step 4: Specific energy and alternate depth calculation;
Es = (y + V²/2g)
where V = Q/A
= Q/bd
Es = (1 + 4.0²/(2x9.81x2))
Es = 1.98 m
Alternate depth,
y2 = Es - d
= 1.98 - 1.0
= 0.98 m
Step 5: Critical depth, minimum specific energy and momentum function;
Critical depth, dc = b (Q²/g)^(1/3) / (1.76)
dc = 2 (4.0²/9.81)^(1/3) / 1.76
dc = 0.67 m
Minimum specific energy, Emin = (Q²/2gA²)^(1/3) + Ks
Emin = [(4.0²/2x9.81x2²)^(1/3)] + 0
Emin = 0.53 m
Momentum function, Mmin = Q √gdc / (1.95b)
Mmin = 4.0 √(9.81x0.67) / (1.95x2.0)
Mmin = 0.81 m
Step 6: Draw typical curves;
The flow depth (d) versus specific energy (Es) and the flow depth (d) versus Momentum Function (M) curve is as follows; Flow depth (d) versus Specific energy (Es) relationship; at d = 1.0 m, Es = 1.98 m and alternate depth, y2 = 0.98 m.
The minimum specific energy occurs at the critical depth (dc = 0.67 m) which is lower than the flow depth.
Hence, the flow is a tranquil flow.
Following are the results obtained in the above steps;
Flow type: Sub-critical (Fr < 1)
Momentum function value: 0
Conjugate depth: 0.7 m, 0.3 m
Alternate depth: 0.98 m
Minimum specific energy: 0.53 m
Critical depth: 0.67 m
Minimum Momentum function: 0.81 m
Question:
If there's a jump formed at 1 m depth;
Starting depth of jump = d = 1.0 m
Finishing depth of jump = conjugate depth
= 0.7 m
Jump height = d - d1
= 1.0 - 0.7
= 0.3 m
Energy loss due to jump = (1/2g)(V2² - V1²)
Energy loss due to jump = (1/2x9.81)(0 - 4.0²/(2x9.81x1))
Energy loss due to jump = 0.81 m
Length of jump , L = 1.0 x Fr2
= 1.0 x 0.902
= 0.81 m.
To know more about Froude number, visit:
https://brainly.com/question/16197137
#SPJ11
The starting and finishing depths of the jump, the height of the jump, the energy loss due to the jump, and the length of the jump depend on these factors.
To calculate the requested parameters and analyze the flow, we will use the principles of open channel hydraulics. Let's go step by step:
Step 1: Calculate the Froude number (Fr) and decide the flow type.
The Froude number is given by:
Fr = V / sqrt(gd)
where V is the velocity, g is the acceleration due to gravity, and d is the flow depth.
Given:
Bottom width (B) = 2.0 m
Flow rate (Q) = 4.0 m^3/s
Flow depth (d) = 1.0 m
First, calculate the cross-sectional area (A):
A = B * d = 2.0 * 1.0 = 2.0 m^2
Next, calculate the velocity (V):
V = Q / A = 4.0 / 2.0 = 2.0 m/s
Now, calculate the Froude number:
Fr = V / sqrt(gd)
The acceleration due to gravity (g) is approximately 9.81 m/s^2.
Fr = 2.0 / sqrt(9.81 * 1.0)
Fr ≈ 0.64
Based on the Froude number, we can determine the flow type:
- Fr < 1: Subcritical flow (Steady flow)
- Fr = 1: Critical flow
- Fr > 1: Supercritical flow
In this case, since Fr < 1 (0.64), the flow is subcritical.
Step 2: Calculate the momentum function (M) and the other conjugate depth (dc).
The momentum function (M) is given by:
M = V * (A / P)^2
where P is the wetted perimeter.
Calculate the wetted perimeter (P):
P = B + 2d = 2.0 + 2(1.0) = 4.0 m
Now, calculate the momentum function:
M = V * (A / P)^2
M = 2.0 * (2.0 / 4.0)^2
M = 1.0
The conjugate depth (dc) is the flow depth corresponding to the minimum momentum function. In this case, dc is equal to the given flow depth (d = 1.0 m).
Step 3: Verify the conjugate depths using the jump formula for a rectangular channel.
For a rectangular channel, the jump formula relates the upstream and downstream flow depths (d1 and d2) with the conjugate depths (dc1 and dc2) as follows:
dc1 * d1 = dc2 * d2
In this case, we have:
d1 = 1.0 m (upstream flow depth)
d2 = ? (unknown downstream flow depth)
dc1 = d = 1.0 m (upstream conjugate depth)
dc2 = ? (unknown downstream conjugate depth)
Using the jump formula, we can solve for dc2:
dc2 = (dc1 * d1) / d2
dc2 = (1.0 * 1.0) / d2
dc2 = 1.0 / d2
Since dc1 = d = 1.0 m, dc2 = 1.0 / d2.
Step 4: Calculate the specific energy (Es) and the other alternate depth (da).
The specific energy (Es) is given by:
Es = (V^2 / (2g)) + d
Calculate the specific energy:
Es = (2.0^2 / (2 * 9.81)) + 1.0
Es ≈ 0.408 m
The alternate depth (da) is the flow depth corresponding to the minimum specific energy. In this case, da is equal to the given flow depth (d = 1.0 m).
Step 5: Calculate the critical depth (dcrit), the minimum specific energy (Emin), and the minimum momentum function (Mmin).
The critical depth (dcrit) can be calculated using the specific energy equation for critical flow:
dcrit = (Q^2 / (g * B^2))^1/3
Calculate dcrit:
dcrit = (4.0^2 / (9.81 * 2.0^2))^1/3
dcrit ≈ 0.443 m
The minimum specific energy (Emin) occurs at the critical depth and is given by:
Emin = (Q^2 / (g * A^2))^1/3
Calculate Emin:
Emin = (4.0^2 / (9.81 * 2.0^2))^1/3
Emin ≈ 0.196 m
The minimum momentum function (Mmin) occurs at the critical depth and is equal to 1.
Step 6: Draw typical curves for flow depth (d) versus specific energy (Es) and flow depth (d) versus momentum function (M).
Unfortunately, as a text-based platform, I am unable to provide visual diagrams. However, you can plot the flow depth (d) on the x-axis and the specific energy (Es) or momentum function (M) on the y-axis using the calculated values from the previous steps. The curves will illustrate the relationships between these variables.
If there's a jump formed at 1 m depth:
To answer the questions related to the jump, we need additional information about the jump type and the channel geometry. The starting and finishing depths of the jump, the height of the jump, the energy loss due to the jump, and the length of the jump depend on these factors.
To know more about hydraulics, visit:
https://brainly.com/question/857286
#SPJ11
