Concept explainers
Repeat Prob. 13-142 for a velocity of 3.2 ms after the hydraulic jump.
The flow rate of water through the gate per meter width.
The flow depth
The energy dissipation ratio of the jump.
Answer to Problem 143P
The flow rate of water through the gate per meter width is
The flow depth
The energy dissipation ratio of the jump is
Explanation of Solution
Given information:
Water is flowing through a sluice gate, the velocity of water before reaching the gate is
The flow is considered per meter width so
The figure below shows the flow.
Figure-(1)
Write the expression for the cross sectional area at
Here, the width is
Write the expression for the cross sectional area at
Here, the velocity at section
Write the expression for the conservation of mass.
Here, the velocity at section (3) is
Write the expression for the Froude number at section
Here, the acceleration due to gravity is
Write the expression for the flow depth.
Write the expression for the conservation of mass.
The flow depth at section (2) is
Write the expression for the Froude number at section
Write the expression for the head loss during jumping.
Here, the velocity at section (2) is
Write the expression for the specific energy before the jump.
Write the expression for the dissipation ratio.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Here Froude number is greater than
Substitute
Substitute
Substitute
Conclusion:
The flow rate of water through the gate per meter width is
The flow depth
The energy dissipation ratio of the jump is
Want to see more full solutions like this?
Chapter 13 Solutions
FLUID MECHANICS (LL) W/CONNECT
- include a free body diagram Seawater is to be pumped into a large tank at a rate of 165 kg/min. The tank is opwn to atmostsphere and the water enters the tank from a 80 m height. The overall efficiency of the motor pump unit is 75 percent and the motor consumes electricity at a rate of 3.2 KW. If the irreversible headloss in the piping is 7 m, the velocity of the water (in m/s) at the tank inlet isA. 6.21B. 7.12C. 8.7D. 5.05arrow_forwardHow is the total mechanical energy of a fluid during steady one-dimensional flow through a wide rectangular channel expressed in terms of heads? How is it related to the specific energy of the fluid?arrow_forwardDuring a retrofitting project of a fluid flow system to reduce the pumping power, it is proposed to install vanes into the miter elbows or to replace the sharp turns in 90° miter elbows by smooth curved bends. Which approach will result in a greater reduction in pumping power requirements?arrow_forward
- 02: Water is to be withdrawn from a 3 m high water reservoir by drilling a 1.5 cm diameter hole at the bottom surface. Disregarding the effect of the kinetic energy correction factor (a = 1). determine the flow rate of water through the hole if (a) the entrance of the hole is well-rounded (K. =0.03) and (b) the entrance is sharp-edged (K, = 0.5).arrow_forwardWhy is the hydraulic jump sometimes used to dissipate mechanical energy? How is the energy dissipation ratio for a hydraulic jump defined?arrow_forwardQ-2 ) ) A boiler house has natural draught chimney of 20 m height. Flue gases are at temperature of 380°C and ambient temperature is 27°C. Determine the draught in mm of water column for maximum discharge through chimney and also the air supplied per kg of fuel. Ans. [11.77 mm of water, 11.32 kg/kg of fuelarrow_forward
- Water is discharged from a dam into a wide spillway to avoid overflow and to reduce the risk of flooding. A large fraction of the destructive power of the water is dissipated by a hydraulic jump during which the water depth risesfrom 0.70 to 5.0 m. Determine the velocities of water before and after the jump, and the mechanical power dissipated per meter width of the spillwayarrow_forwardA cylindrical tank is being filled with water flowing with constant velocity V1 through a tap (Tap 1) that has an opening of diameter D1. The tank is initially empty and contains a tap (Tap 2) placed H1 m above the bottom of the tank that drains waterat a velocity of ? = √2?h. Assuming flow through Tap 2 starts the moment Tank 1 2height reaches H1 m, write the differential equation governing the change of water level inside the tank with time (?h =? );??i) Before water level reaches H1.ii) After water level reaches H1 up until the tank is full.Do NOT attempt to solve the differential equations!Just drive the differential equations and write the boundaries of the definite integrals.arrow_forwardDetermine the mean velocity, if the maximum velocity after comparing velocity relation is 5.5 m/s. _____ m/sarrow_forward
- What is the Stefan-Boltzmann Law? Distinguish between black and gray body What is the hydraulic diameter? Where is it used? Distinguish between Biot number and Nusselt number.arrow_forwardFor the discharge coefficient C, What else factors can influence its magnitude besides the diameter?arrow_forward5 - Water at an effective pressure of 120 kPa flows through a horizontal pipe at a speed of 1.15 m/s. The pipe outlet is oriented 90° upwards with an elbow. What is the maximum height at which water can rise in this way? a) 9.4m B) 12.4 m NS) 11.5m D) 7.8m TO) 6.9marrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning