A weir is an obstruction in a channel flow that can be calibrated to measure the flow rate, as in Fig. P5.32. The volume flow \( Q \) varies with gravity \( g \), weir width \( b \) into the paper, and upstream water height \( H \) above the weir crest. If it is known that \( Q \) is proportional to \( b \), use the pi theorem to find a unique functional relationship \( Q(g, b, H) \).### Diagram Explanation:- **Diagram Layout**: The diagram illustrates a side view of a channel with a weir. - **Water Flow**: The water flows from left to right, approaching the weir.- **Weir Representation**: The weir is depicted as an obstruction, causing the water level to rise upstream, with the height \( H \) noted above the crest of the weir.- **Measurements**: - \( H \): Height of the water above the weir. - \( Q \): The volumetric flow rate of water over the weir.- **Arrows**: Indicate the direction of water flow before and after the weir. This setup is used to determine the relationship between the flow rate \( Q \) and the parameters \( g \), \( b \), and \( H \) using dimensional analysis.

Given- The volume flow rate depends upon on gravity,weir width and upstream water height. Therefore…

A weir is an obstruction in a channel flow that can be cali- brated to measure the flow rate, as in Fig. P5.32. The vol- ume flow Q varies with gravity g, weir width b into the paper, and upstream water height H above the weir crest. If it is known that Q is proportional to b, use the pi theorem to find a unique functional relationship Q(g, b, H).

A weir is an obstruction in a channel flow that can be cali- brated to measure the flow rate, as in Fig. P5.32. The vol- ume flow Q varies with gravity g, weir width b into the paper, and upstream water height H above the weir crest. If it is known that Q is proportional to b, use the pi theorem to find a unique functional relationship Q(g, b, H).

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: (a) The upstream face of a dam is curved and is part of a circle of radius 10 m. and holds back…

Q: A concrete pipe of 6 m long is used to block flood water from the left to contaminate a pond of oil…

A: Objective: To determine the magnitude and direction of the resultant force on the concrete pipe.…

Q: Q2(a) A river discharges flow at 2 m^3/s/m at depth of 1.1 m. A 0.25 m high broad-crested weir is…

A: Schematic diagram of the given problem:

Q: What does a negative flow rate mean? A. This value is incorrect and shall be indicative of wrong…

A: The negative flow rate means that it is backflow. The negative flow rate indicates the direction of…

Q: Question 3: In a rectangular channel shown in the figure, water flows at a rate of (5 + a/2) m/s. a)…

Q: A trapezoidal channel with a bottom width of 10 m carries a flow of 1000 m/s. The side slope z = 2,…

A: Aside from the perplexing number related we do to observe that best cross part of a channel for an…

Q: Tutorials - Sediment Transport 1. A European river has the following hydraulic characteristics: Flow…

A: Given Data:Discharge: Q= 450m3/s,Width b= 50mFlow depth h= 6mBed Slope i= 0.0003.diameter d= 0.01m

Q: Assignment 1. Derive from first principle the chezy equation for uniform flow. tieely

Q: A rectangular and horizontal channel with a width of Bo = 3 m and water depth of y1 = 1.38 m carries…

Q: The dam and flow nets shown in Figure below. The dam has two 10 m sheet piles driven partially into…

A: Given:-Length of sheet piles drivenCoefficient or permeability, To determine:-i) The quantity of…

Q: Question 1 The sketch below represents a trapezoidal open channel used to manage storm water in A…

Q: If the designed dam is 12m height. what would be the bottom width of the dam?

A: Given Equation W=0.2H+2.1 H=12 m

Q: A channel with a section as shown carries 1.1 m'/s of water with the depth as shown. The slope of…

A: Given:- The discharge of the water = 1.1 m3/s The depth of the water = 1.1 m The width of the…

Q: expansion transition for a canal by Mitra's Consider the following data while designing an method:…

Q: Many catastrophic failure occurred in geotechnical engineering due to instability of soil mass.…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: b) The screw-down vertical gate G of width b installed at a stormwater channel (Figure 2) is…

A: solution: Given: Q=25m3/s b= 4m Yu=6m Fgd=500kN Force by moment Equation: F=γ.Q.Vx The above…

Q: n a trapezoidal channel there is a dam that produces a backwater curve with a height of 0.5 m, as…

A: step 1-

Q: A) what is the number of drop of the flownet? B) What is the flow of water in the unit of cm^2/min?…

A: The given figure shows a concrete dam on-site and its corresponding flow net.The coefficient of…

Q: In a wastewater treatment plant, primary sedimentation tank (PST) designed at an m’/day/m² is y 3…

Q: A rectangular channel carries a discharge of 80 m³/s. The median particle diameter of the suspended…

A: The shape of the channel is rectangularThe discharge through the channel is,The mean size of the…

Q: The bottom slope of an open channel with cross-section A at point A is I = 0.0005. Calculate the…

A: The bottom slope of the channel (S) = 0.0005width of the channel (B) =6mheight of channel (H) =…

Q: weir installed at the end of a rectangular channel controls the flow of water. The rate of flow is…

A: To find percentage error in discharge measured

Q: 3.1. A trapezoidal channel convey 15 m³/s of water on a bed slope of 1 in 200. The base width of the…

A: As per our guidelines we are supposed to answer only one question. Kindly repost the other questions…

Q: Manning's equation is Q = where Cm AR 2/3 1/2 n Q = Cm = = flow (m³/s) 1.49 USC system 1.00 SI…

A: D = 275.3317482 8/3√(Qn/S1/2)Explanation:

Q: An irrigation canal with a given cross-section is desired to be dimensioned hydraulically in the…

A: m = 2 Manning's coefficient = n = .025 Base slope = S = .008 D = 2m f = .03

Q: A channel carries irrigation water at an average velocity of 2 m/s. The channel is 650 m long, 2 m…

A: Given, Average velocity in irrigation channel, VP = 2m/s Length of channel, LP = 650m Depth of…

Q: A rectangular channel with a width of Bo = 3 m and water depth of y = 1.41 m carries a discharge of…

A: Width of channel (Bo) = 3m Depth of flow (y) = 1.41 Discharge (Q) = 0.8 m3/s Determine the momentum…

Q: The ratio of the upstream depth to downstream depth in a hydraulic jump for a rectangular,…

Q: Question 2. The stream function for a given two-dimensional flow field is = 5x²y (5/3)y³ a) Is this…

Q: Water flows over the spillway shown in the figure below. If the velocity is uniform at sections (1)…

Q: A weir installed at the end of a rectangular channel controls the flow of water. The rate of flow is…

Q: 1 m 2 m 2 m 1m 2 m 4 m 3 m

Q: The figure shown is a cross-section of a cast iron pipe with coefficient of roughness n = 0.012. If…

Q: A concrete channel, rectangular in shape, is laid on a channel bed of slope 0.0010. At an upstream…

A: Given data Wide, b=4.5 mDepth at upstrem, d1=1.5mDepth at downstream, d2=1.17 mLength, L=300mSlope,…

Q: An upstream channel enters a horizontal channel at a discharge of 792 cfs. The upstream channel has…

Q: Consider a rectangular channel with an aspect ratio greater than 5 (width B and depth zo). The…

A: Aspect ratio = 5 velocity distribution is u=K1z To find 1) Average velocity for the cross section.…

Concept explainers

Highway Drainage

Highway drainage is the process of extracting and regulating the excess surface water on the pavement by giving the desired slope. The construction of a highway drain helps to divert the water present on the surface, and sub-grade by the means of slope. Highway drainage systems are a necessary part of smooth functioning of traffic, since the highway drainage systems provide proper disposal of unwanted substances from the highways.

Question

A weir is an obstruction in a channel flow that can be calibrated to measure the flow rate, as in Fig. P5.32. The volume flow \( Q \) varies with gravity \( g \), weir width \( b \) into the paper, and upstream water height \( H \) above the weir crest. If it is known that \( Q \) is proportional to \( b \), use the pi theorem to find a unique functional relationship \( Q(g, b, H) \).

### Diagram Explanation:

- **Diagram Layout**: The diagram illustrates a side view of a channel with a weir.
- **Water Flow**: The water flows from left to right, approaching the weir.
- **Weir Representation**: The weir is depicted as an obstruction, causing the water level to rise upstream, with the height \( H \) noted above the crest of the weir.
- **Measurements**:
- \( H \): Height of the water above the weir.
- \( Q \): The volumetric flow rate of water over the weir.
- **Arrows**: Indicate the direction of water flow before and after the weir.

This setup is used to determine the relationship between the flow rate \( Q \) and the parameters \( g \), \( b \), and \( H \) using dimensional analysis.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Consider the one-dimensional open channel flow shown in Figure P10.8. (a) Using the continuity principle and Bernoulli’s equation, show that where F is the local Froude number. (b) Discuss the implications of this result for subcritical flow everywhere, supercritical flow everywhere, and for F = 1 at station 2.
The figure shown is a cross-section of a cast iron pipe with coefficient of roughness n = 0.012. If the slope of the channel bed is 1.8 m for every 1 kilometer of its length, determine the following: a. Wetted perimeter of the section, P b. Hydraulic radius, R b. Flowrate, Q
ANSWER URGENTLY
HYDRAULICS Convert all units in SI. Round off to 2 significant figures. Use Francis Formula. A rectangular channel 20 ft wide has a 3 ft depth of water flowing with a mean velocity of 2.45 ft per sec. Determine the height of standard sharp-created weir that will increase the depth in the channel of approach to 5 ft.
A triangular threshold is used to control the water depth which tends to be constant upstream of an open channel. Water flows on a V-notch weir with = 90^o and the magnitude of gravity is 9.81 m/s^2. What is the water discharge upstream of the threshold when conditions are normal with a water level of 0.24 m and during a flood with a water level of 1 m?
The cross-section of a navigation channel is shown in figure. A I J B/ 4m D E F 30 m 30m'6m 6m 8'm *20m 150 m 20m Channel section Determine the discharge through the channel if the depth of flow is 12 m. The channel has a slope of 1 in 2000 and the Chezy's constant C is 45.
2. Water flows over a sharp-crested triangular weir at a rate of 0.28m/s whose vertex angle 60°. Find the percentage of error in the computed value of the flow if the head measurement had been incorrectly observed as being 0.006m greater than its value. Use C = 0.58. Draw the sketch.
Figure 4. Problem 4 Illustration. Problem 5. Bonus Question: Reynolds Transport Theorem. The rectangular channel shown is 1.5 m wide. What is the discharge in the channel? Vertical depth 1 m u = 3 m/s Water 30 Figure 5. Problem 5 Illustration.
a water resource engineer is in charge of designing atrapezoidal open channel for flood control. Typically, these types of channels are made ofconcrete. Use Manning’s Equation.Flowrate (Qb), channel slope (S0), bottom width (Bw), channel sidewall angle (θ), actual depth(y), and Manning’s coefficient (n) are tabulated below. State all assumptions. * z is the sidewall ratio: for every 1 unit increase in depth, the top width increases by z on eachside of the channel, or 2z total.A) Given the actual depth, y = 1.25 ft, find the discharge Qa.B) Find the Critical Depth, yc, for the discharge Qa found in (a). For a trapezoid,dA/dy =Bw +2 yz .Is the flow sub- or super-critical?C) Determine the uniform flow normal depth (yn) at Qb = 209 cfs.D) If the slope is increased to 0.001, what roughness coefficient would be needed tomaintain the same discharge Qa? What about for Qb? Would it be the same value?
Kindly do not give copied or wrong solution.
A trapezoidal channel with uniform flow depth 4 m. The base width is 6 m and the side slopes are equal to (1V:1H), Manning's n can be taken as shown in the figure. What is the weighted Manning's coefficient using Horton's equation. n=0.019 n=0.022/|1 n=0.012