Innovative Detection of Image Manipulation via Lateral Chromatic Aberration Anomalies

Abstract

In a flow through pipe system design we are considering the various perimeters which are related to our design system to define the approximation results. In this design methodology of the pipe system we are defines the major as we as minor losses, frictional head loss and pressure gauges as an important perimeters by keeping the hydraulic parameters within an acceptable range cannot by itself to fulfill these requirements. The hydraulic design of water transport and distribution system requires through calculations due to the significant impact of each components on the overall operation.

Hydraulic design primarily deals with pressure and hydraulic gradients. In addition, the flow velocities, pressure and flow fluctuations are also relevant design factors.

Introduction

The design of the water transport system consists of two parts: hydraulic and engineering. Opting for a large diameter, reservoir volume or pump unit will always offer more safety in supply but implies a substantial increase in investment cost. The pressure criterion is usually formulated as the minimum/maximum pressure required or allowed, at the most critical point of the system.

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Water flow to any discharge point choosing the easiest path: either the shortest one or the one with the lowest resistance.

Optimal design from the hydraulic perspective results in a system that demands the least energy input for water conveyance. It should not be forgotten that the most effective way to reducing the friction losses, by enlarging the pipe diameters, consequently yields smaller velocities. Hence it may appear difficult to optimize both the pressure and velocities in the system.

Furthermore, in system where reliable and cheap energy is available, the cost calculations may show that the lowest investment in pipes and reservoir justifies the increased operational costs of pumping.

Construction of design pipe line between reservoir to water tank. In this above figure we are going to design flow system which supply water using pump from reservoir to the supply tank. Here in designing figure we know the how much flow rate is passing through the pipe line and the length of the pipe we can easily observed. In pipe we are considered the several losses which occurring inside the pipe which is directly related to the, what kind of material we are using for pipe construction.

Under the following assumptions which is: flow along the stream line, steady flow, inviscid fluid flow and incompressible flow states that summations of all the energy(pressure energy, kinetic energy, potential energy) per unit weight between any point is constant, is derived by Bernoulli’s. Which is also called as a total head of energy.

Friction factor of commercial pipes can be calculated using the general equation for the laminar and turbulent flow. In the transition region friction factor depends on both Reynolds number and the relative roughness (e/D). However, the friction factor of the commercial pipe in this zone can be calculated using an Colebrook-white formula. Frictional head loss, major and minor head loss considered during the design of pipes.

Calculations and Results

Flow under the pipe assuming as a turbulent flow, although generally flow through pipe taking as a turbulent flow. So, first step to applying the Bernoulli’s equation between section 1 and 2 see in the above figure.

The assumptions we are taking here as described as:

• Here in pipe design system we are considering the all major and minor losses throughout the system.
• Density of the water taking 1000kg/m3.
• Analysis of the above figure P1=P2=Patm which is neglected.
• Also taking the datum as section 2, we found their Z1-Z2=50m.
• In frictional head loss between the cast iron pipe, assuming the flow is turbulent and the Darcy friction factor (assuming) f = 0.03.
• Neglecting the major losses between the pipe sections due to the crucial calculation aspects.
• The major losses of the pipe bend section and the inlet section of the pipe.
• And are the major losses of the pipe valves losses on the pipe section, which are located at the inlet and outlet sections.
• Total length of the pipe is 350m.
• Here we are designing for the different diameters of pipe for the different materials as well so we only know the roughness value of the pipe in Colebrook-white equation so we are neglecting this formula for designing pipe.
• Both The initial velocities zero before the starting of work.

Calculation for Cast Iron Pipe Design Diameter

Now substituting the value in above equation we have:

50 =

Now the flow rate formula Q = A*V with the help of this arranging the equation in terms of diameter of pipe. (A = D2)

Now after solving the above equation we have:

Design diameter of the cast iron pipe is D = 445.254mm ≈ 446mm (approx.)

Calculation for asphalt cast iron pipe design diameter:

Followed the above all the assumption for asphalt cast iron pipe, only In frictional head loss between the asphalt cast iron pipe, assuming the flow is turbulent and the Darcy friction factor (assuming) f = 0.04.

Now substituting the value in above equation we have:

50 =

Now after solving the above equation we have:

Design diameter of the asphalt cast iron pipe is D = 471.623mm ≈ 472mm (approx.)

The pumping power required for the pump P = ρgQHf

Substituting the values P = 1000*9.81*1*50 = 490500W

1 HP = 746 watt

So pumping horsepower P = 657.506hp

Table 1: Pipe Material and Design Specifications

Table 2: Major and Minor Losses in the System

Table 3: Assumptions and Parameters

Table 4: Bernoulli’s Equation and Pump Power Calculation

The tables comprehensively outline the design parameters, material specifications, and hydraulic calculations involved in the water transport system's planning and optimization process. This structured approach ensures a balance between efficiency, cost, and hydraulic performance, guiding the development of a reliable water supply infrastructure.

Conlcusion

In this designing problem of the pipe as per the assumptions which I made getting the satisfactory results as per the calculation criteria. In cast iron pipe with the .03 of the Darcy friction factor we got the smaller diameter and high inlet velocity as compare to the asphalt cast iron with the .04 Darcy friction factor value. As we easily observed that higher the diameter smaller the flow velocity and smaller the diameter grater the flow velocity. So our construction for the pipe from the reservoir to the elevated water supply tank is feasible, because the assumptions which we made correct according the results we got, also we define the head loss, pumping power and inlet velocities for reservoir and supply tank.