CVL502 Lab #6 Sluice Gate and Specific Energy PDF (final)

1 8) Sluice Gate and Specific Energy Background The total energy for a flow is calculated from (1) the depth of water in the flow, (2) the pressure component, and (3) the kinetic energy component related to the velocity of the flow moving through the channel. This is described by the Bernoulli equation between two points 1 and 2, along a streamline, as: (1) P 1 γ + Z 1 + V 1 2 2 g = P 2 γ + Z 2 + V 2 2 2 g + h L where P = pressure, in N/m 2 γ = unit weight of water, in N/m 3 Z = elevation, in metre V = average flow velocity, in m/s g = gravitational acceleration = 9.806 m/s 2 In most applications, the head loss, h L , may be assumed to be negligible when the viscosity and the distance between the two points are not too big. In addition, for an open channel flow that is open to the atmosphere, the absolute pressure can be considered equal to the atmospheric pressure, so the gage pressure is zero. As a result, the following simplified energy equation is obtained: (2) Z 1 + V 1 2 2 g = Z 2 + V 2 2 2 g For a rectangular channel with flow depth y, the flow velocity can be related to a discharge rate per unit width, q, such that: (3) q = Q B = AV B = yV or V = q y where Q = volumetric flow rate, in m 3 /s B = width of the channel cross section, in m A = cross-sectional area of the channel, in m 2 y = depth of the cross section, in m q = unit discharge, defined as discharge per unit width, in m 3 /s/m Substituting Eqn. (3) into Eqn. (2), and taking the elevation above the datum as the depth of the flow, one arrives at the specific energy (E) equation as follows:

2 (4) E = y 1 + q 2 2 gy 1 2 = y 2 + q 2 2 gy 2 2 For a given unit discharge (i.e. q = constant), the specific energy diagram is illustrated in the following figure. Note that for each value of unit discharge, there is an associated critical depth, y c , which corresponds to the minimum energy. Flow with a depth greater than the critical depth is called “subcritical”, and flow with a depth less than the critical depth is called “supercritical”. Subcritical flow has a larger potential energy component, and supercritical flow has a larger kinetic energy component. When the scale of the x and y-axes are identical, the y = E line is at 45° and forms the upper boundary of the specific energy curve. In addition, the dimensionless Froude number is defined as follows: (5) Fr = V gy = q y gy = q gy 3 And it can be demonstrated that: Fr = 1 at critical conditions, Fr < 1 at subcritical conditions, and Fr > 1 at supercritical conditions. For a given energy value there will generally be two possible depths, a subcritical depth and a supercritical depth. These depths are called the alternate depths, and may be derived by solving (E min , y c )

3 Eqn. (4). As the critical depth occurs at the minimum specific energy, we can take the first derivative of the energy equation with respect to depth (dE/dy) and equate it to zero, to determine the critical depth, y c , for each unit discharge, q: (6) y c = ( q 2 g ) 1/3 This value may be substituted into Eqn. (4) to obtain the minimum energy, E min . (7) E min = 1.5 y c Objective The objective of this experiment is to study the concept of specific energy in open channel flow with the control of the opening of a sluice gate. Equipment 1 open flow channel with sluice gate control (shown in Figure 1) 1 stop watch 1 measuring tape 1 hydraulics bench