The equation 1 shown below is the one dimensional Bernoulli's equation. This formula is a simplified teady state form and in the direction of flow that can be used and applied to a specific streamlines and to flow sections along a conduit as well. The Bernoulli's equation is often coupled with the one-dimensional, compressible steady state flow rate shown in equation 3. whom 2/+P +2₁ = 2g 22 2g Y H= v P2 + 2g Y +22 (1) (2)

The equation 1 shown below is the one dimensional Bernoulli's equation. This formula is a simplified teady state form and in the direction of flow that can be used and applied to a specific streamlines and to flow sections along a conduit as well. The Bernoulli's equation is often coupled with the one-dimensional, compressible steady state flow rate shown in equation 3. whom 2/+P +2₁ = 2g 22 2g Y H= v P2 + 2g Y +22 (1) (2)

Principles of Foundation Engineering (MindTap Course List)

8th Edition

ISBN:9781305081550

Author:Braja M. Das

Publisher:Braja M. Das

Chapter14: Sheet-pile Walls

Section: Chapter Questions

Problem 14.9P

See similar textbooks

Similar questions

The flow through a rectangular channel (width in x and height in z) is nonuniform with a velocity profile of V(z) = mz+b. The velocity at the floor of the channel is V(z=0) and the velocity at the top of the channel is V(z=Z). a) Develop an expression for flow rate and average velocity using the given constants. If the channel is 5m wide in x and 3m tall in z and V(z=0) = 0 m/s and V(z=3m) = 6 m/s: b) Determine the value of the constants m and b in the velocity profile c) Determine the value of the flowrate and average velocity of water in the channel.
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.
Given is the flow of a channel of large width b under asluice gate, as in Fig.. Assuming frictionless steadyflow with negligible upstream kinetic energy, derive a formulafor the dimensionless flow ratio Q2/(y 31b2g) as a functionof the ratio y2/y1. Show by differentiation that themaximum flow rate occurs at y2 = 2y1/3.
Use the Cauchy-Reiman Eq. and Darcy’s Law in terms of the discharge potential to prove that the Φ and Ψ functions (given below) for uniform flow are correct. Φ= -Qx0X - Qy0YΨ= -Qx0Y + Qy0X
an incompressible plane flow has the velocity potential φ = 2Bxy, where B is a constant. find the stream function of this flow, sketch a few streamlines, and interpret the flow pattern.
Subject : Fluid mechanics Water flows in a rectangular channel at a depth of 2.0 m and velocity of 1.0 m/s. The discharge of water is suddenly trebled. Find the increased depth of flow.
A channel is used to carry storm water into the ocean (Fig. 1). The channel is made of cement with neat surfaces, and its bed drops 1 ft per 1 000 ft. 1. Given the water depth h is 2 ft at the deepest portion of the channel. Calculate its flow rate using the Chézy equation and Manning's formula. 2. Suppose that the flow rate in the channel is doubled due to a recent storm, is the channel deep enough such that the water does not spill over?
Water flows through a pipe AB 1.2 m diameter at 3 m/s and then passes through a pipe BC 1.5 m diameter. At C, the pipe branch. Branch CD is 0.8 m in diameter and carries one third of flow in AB. The flow velocity in branch CE is 2.5 m/s. Find the mass rate of flow in AB, .
Water flows through a pipe AB 1.2 m diameter at 3 m/s and then passes through a pipe BC 1.5 m diameter. At C, the pipe branch. Branch CD is 0.8 m in diameter and carries one third of flow in AB. The flow velocity in branch CE is 2.5 m/s. Find the mass rate of flow in AB, Solve it early
For type S2, one of the water surface profiles in a variable flow environmenta) Show the schematic position of the profile.b) Determine the sign of the profile.c) Determine the flow of the current depth according to the limit values and show it by drawing a figure.
1. A rectangular channel has a contraction that smoothly changes the width to a minimum width of 1.5 f t (the throat). If the flow is critical at the throat, find the volume flow rate when the depth at the throat is 1.5 f t. 2. Water in an open channel of constant width flows over a bump of height 1 f t, as shown in Figure P10.10. What is the depth of the water Y2? Assume uniform flow of constant width with no losses.
Consider fully developed, two-dimensional channel flow—flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in Fig. (dP/dx is constant and negative.) The flow is steady, incompressible, and two-dimensional in the xyplane. The velocity components are given by u = (1/2? )(dP/dx) (y2 − hy) and ? = 0, where ? is the fluid’s viscosity. Generate an expression for stream function ? along the vertical dashed line in Fig. For convenience, let ? = 0 along the bottom wall of the channel. calculate the volume flow rate per unit width into the page of Fig. P9–48 from first principles (integration of the velocity field). Compare your result to that obtained directly from the stream function. Discuss.