A water tank used for fire fighting is shown in the figure. A fire extinguishing installation was installed by the cast iron pipe (roughness value ε=0.005mm) from the steady, incompressible water flow for pipe length Lpipe=126.2 m and pipe diameter D=106.2 mm. The height of the tank from the pipeline is h= 24.62 meters. A gate valve is placed on the end line of the installation. Accept that the local pressure loss equivalent length of the gate valve is given as Le/D=8.62, neglect other local pressure losses in the pipe line installation. In places 1 and 2 shown in the figure, the pressure is atmospheric pressure. i-Accordingly, calculate the speed, volumetric flow rate and mass flow rate of the water when the gate valve is opened in this installation. Repeat the calculation at least three iteration, if necessary, you can do more iteration. (ii) Calculate how much electrical energy can be produced if a hydraulic turbine with a total efficiency of 7a.b% is placed in front of the valve when the gate valve is opened at constant water level in the tank. Take the kinetic energy correction coefficient 1. Solve the problem by making the necessary assumptions and drawing the schematic figure
A water tank used for fire fighting is shown in the figure. A fire extinguishing installation was installed by the cast iron pipe (roughness value ε=0.005mm) from the steady, incompressible water flow for pipe length Lpipe=126.2 m and pipe diameter D=106.2 mm. The height of the tank from the pipeline is h= 24.62 meters. A gate valve is placed on the end line of the installation. Accept that the local pressure loss equivalent length of the gate valve is given as Le/D=8.62, neglect other local pressure losses in the pipe line installation. In places 1 and 2 shown in the figure, the pressure is atmospheric pressure.
i-Accordingly, calculate the speed, volumetric flow rate and mass flow rate of the water when the gate valve is opened in this installation. Repeat the calculation at least three iteration, if necessary, you can do more iteration.
(ii) Calculate how much electrical energy can be produced if a hydraulic turbine with a total efficiency of 7a.b% is placed in front of the valve when the gate valve is opened at constant water level in the tank. Take the kinetic energy correction coefficient 1.
Solve the problem by making the necessary assumptions and drawing the schematic figure
(1)
It is given that,
The total length of the pipe is
Apply Bernoulli's equation between section 1 and 2,
Here hL is the head loss.
Given that,
First iteration,
Assume the friction factor to be 0.02
Then the velocity of the flow is
From the moody’s chart,
Second iteration,
Take f = 0.022
Then the velocity of the flow is
Reynolds number of flow,
From the moody’s chart,
Step by step
Solved in 5 steps with 16 images
