Problem 4: Control Volumes and Bernoulli's equation Water (density p) flowing at speed V in an open channel of depth h goes through a change H in elevation (Figure 4). Downstream of the elevation change, the depth of the channel decreases to h/2. Vo Fx H V h/2 Figure 4: Open channel undergoing an elevation change. 1. Find the flow velocity V downstream of the elevation change. 2. Find the change in elevation H. 3. Find the horizontal hydrodynamic force Fx exerted by the flow on the bottom of the channel.

Flow Speed in a Channel The speed of water flowing in achannel, such as a canal or river bed, is governed by theManning Equation,

Inflow depth= h, hwater Water from a storm drain flows over an outfall with a height, h, = 0.25 m, and width into the paper of B = 5.0 m. The inflow has a velocity, Uin = 2.0 m/s, into a tank. You can assume that the water instantly spreads out over the surface in a smooth fashion so that the water level in the tank can be considered a flat surface of area A=BxL. At the bottom of the tank is a porous bed that absorbs the water at a uniform vertical velocity of V = 14.0 mm/s, as shown in the figure given below. The outflow at the bottom of the tank, Qout m³/s is equal the volume flux of water entering the filtration layer. The tank is B = 5.0 m deep into the paper and has a length L = 25.0 m. There is an initial depth of water on top of the porous bed of ho =29.0 mm. Find the height of the water, h,water (the ponding level) above the porous media at t = 11.0 seconds after the start of the storm. Please provide your answers to 5 significant figures. h = m

PLEASE BOX YOUR ANSWERS Problem-3 The water flowrate, Q in an open rectangular channel is a function of height, H, the channel width, b, and gravity, g. In a lab test it was determined that if b = 3 ft = 1.96 ft/s. Take H and g as repeating variables to determine an equation for the flowrate if it known that Q is directly proportional to the channel width, b. and H = 4 in., then Q

Three reservoirs are connected by a piping system as shown in Figure 1. Find the discharge into or from the reservoir B and C, if the rate of flow from reservoir A is (55+X) liter/s. Also find the height of water level in reservoir C. Assume the following data: Pipe 1 2 3 Length (m) 1X00 600 700 Diameter (mm) 400 300 200 Friction factor 0.008 0.008 0.008

3. (a) 3. (b) As shown in Figure P3(a), water flows in a rectangular channel which is 5.0 m wide. The upstream depth is 60 mm. The water surface rises by 40 mm as it passes over a portion where the channel bottom rises by 15 mm. Neglecting viscous effects, what is the volume flowrate Q? [Ans: 0.390 m³/s] Q 9 V₁ = 10 m/s 60 mm Figure P3(a) As shown in Figure P3(b), water flows up a ramp with negligible viscous losses. The upstream depth and velocity are maintained at h₁ = 1 m and V₁ = 10 m/s, respectively. The ramp height is H = 2 m. Obtain an expression for the downstream depth h₂. Optional: Solve for possible values of the downstream depth h₂. [Ans: 19.62h2 -80.38h2 +100=0; h₂= 3.731 m, 1.366 m] 9 h₁=1 m 100 mm Figure P3(b) 15 mm ņ2 H = 2m V₂

The volume flow Q over a certain dam is a function of damwidth b , gravity g , and the upstream water depth H abovethe dam crest. It is known that Q is proportional to b . If b=120 ft and H =15 in., the flow rate is 600 ft 3 /s. What willbe the flow rate if H = 3 ft?

This very large reducing bend is in a vertical plane. Water is flowing. Diameter at 1 is 6 ft., diameter at 2 is 4 ft,, discharge Q is 300 cfs, and pressure at 1 is 40 psi. Neglect headloss. a) Find p2 ​in psi, and b) Find Fx​, the force (vector) of the pipe bend on the water, x​ direction only: This is an energy and momentum problem. only HANDWRITTEN answer needed ( NOT TYPED)

1)A wave with a period T = 10 seconds is propagated shoreward over a uniformly sloping shelf from adepth d = 656 ft to a depth d = 9.8 ft. Find the wave celerities C and lengths L corresponding to depths d =656 ft and d = 9.8 ft 2) A wave in a depth d = 12 m, height H = 3 m, and a period T = 10 sec. The corresponding deepwaterwave height is H0 = 3.13 m.Find:(a) The maximum horizontal and vertical displacement of a water particle from its mean position when z= 0 and z = -d.(b) The maximum water particle displacement at an elevation z = -7.5 m when the wave is in infinitelydeep water.(c) For the deepwater conditions of (b) above, show that the particle displacements are small relative tothe wave height when z = -L0 /2 3)A concrete coated steel gas pipeline is to be laid between two offshore platforms in 100 m water depthwhere the maximum environmental conditions include waves of 20 m wave height and 14 s period. Thepipeline outside diameter is 46 cm, and the clay bottom slope is 1 on…

G1/ In the fig.shown, the Flow rate Pipe (A) is equal ( QA = 25 Lit15), the diameter is equal ( DA = 75 mm, D, = De = Dc =30mm), and the velocity in Pipe (D) is equal (Uo=5 m/s), the relation between flow rate in in 6o mm, Pipe (B) and pipe (c) GB =3 Qc. Find the Value of '. Re, Qc, Qo. 2- UA, UB, Uc: Pe = 30 mm water Pc = 30mm imput QA = 25 2i+/sec OA= 75 mm = 6o mm input = A outPut = B, C, D accumulation = o.