## Formula for Work Done and Efficiency – Hydraulic Turbines – Fluid Mechanics

Do subscribe to Ekeeda Channel and press bell icon to get updates about latest engineering HSC and IIT JEE main and advance videos So after seeing the constructional features let’s move to the velocity triangle and the work done and the efficiencies of Francis Turbine so we’ll see the velocity triangle for transistor bind as you saw for Pelton wheel in Pelton wheel The triangle was different here now in this case and Francis it’s Different because you know that the Inglot is radial in Francis turbine and the outlet is action so the triangle looks something different here know so I draw the triangle is let it out so I’ve drawn the runner so picking based on this runner will drop other triangles you so after on the triangle v1 is the inlet velocity absolute velocity piglet v r1 is the relative velocity at inlet u1 is the blade velocity at the inlet side v r2 is the relative velocity at the outlet v2 is the outlet velocity absolute of velocity u would be u2 u2 is the blade velocity at outlet so after saying the velocities we will see the angles now so alpha is the inlet blade angle we can call it the guideway Knakal which is the angle made by the absolute velocity with the horizontal cheetah is the Angle made by the relative velocity for the London sigh and beat up here as you can see here since the velocity at the outlet is axial v2 has to be the beta has to be 90 degree and we do has to be drawn perpendicular so this is how the triangle looks like for a long sitting this saw the beautiful triangle looks like a Francis turbine the beautiful U is always 90 degree or is always 90 degree in case of an axis turbine now comes the volume velocity and the flow velocity if we all know that the world below Scylla T is nothing but the component of the absolute velocity okay let’s do one thing let’s cut the util of the triangle separately and see you so what velocity and slow velocities are nothing but their components of the absolute velocity rate a minute so the horizontal component of absolute velocity and it gives you the velocity attended and the vertical component of the absolute velocity relative to the flow velocity editing now let’s see the same thing for the outlet but on CD attractions you as you can see you’re the absolute velocity at Inlet was in planned an outlet triangle the absolute velocity after it is vertical since it is vertical you cannot have components of it so the horizontal component of the velocity at the outlet is zero so it’s a very important part of this Francis turbine the world velocity at the outlet is zero and the vertical component itself is the flow velocity so V 2 is not is VF 2 n V W 2 is 0 so this is a very important statement that I’m making you and Francis turbine the wall velocity at outlet is 0 since the flow is along the axis there is no component horizontal component along B of the V 2 so one of the law sitting has to be 0 so that was all about this diagram the velocity triangles let’s move on to the workplane formulas for Francis turbine so let’s look at the work done by the jet on the plant system and so before directly moving on to the Waltons let’s go step by step let’s look what is the force exerted by a paycheck on the impulse turbine so the formula remains the same for the force exerted as we see as you saw for Pentonville as we saw and in fact objects the food exerted by our jet of water onto a field is given by this is a very basic formula that we have already seen that you’ve been saying through our this subject so the force exerted by the jet is Rho AV 1 VW 1 plus VW 2 so this is the force exerted by the jet of water onto the runner since here it is rotating let’s see what will be the talk so once you know the force you can get 12 by multiplying it with radius since the radius is different at Inlet and outlet will be having r1 r2 as it goes in it when it becomes harder and harder to now after getting talks from foals once you know talk you can get work done so the formula is basic formula for Walden is torque into Omega in angular motion in as in linear motion we have work is force into distance similarly angular motion we have is T into Omega so we know the value of torque we know the value of Omega let’s multiply and get the value of done you now our 1 into Omega is nothing but linear velocity we all know that these are the winner so r1 times Omega gives linear velocity of the plate at the inlet and r2 omega gives you the linear velocity of the plate at the outlet so this is the formula for work done and next we’ll see what is efficiency and once we know the work done we can easily get at the efficiency value so we’ve got the value of work done we saw where this pose after force we got to talk so we got the value of talk and once you get talk after you multiplied talk with the velocity a great work now this work done by good earner is known now we’ll move on to getting efficiencies so before moving on to efficiencies let’s do some manipulations in this formula as I’ve already said earlier the value of the world component at outlet for Frank sister minus zero so let’s eliminate it do only so the Francis turbine VW is zero we all know that we have already seen that so let’s put zero for that and see what the formula becomes you so the formula for work done per second is ro everyone will de l’eau anyone next is the hydraulic efficiency hydraulic efficiency nothing the same formula holic efficiency is nothing but the power developed by the Ronna and divided by the power input to the runner you so the power as nothing but what worked and boss again Colburn per second we call it power and the power output is nothing but sorry power developed is nothing but Rho everyone will degrow anyone and power input is nothing but Rho gqh you can cancel the light turns here Rho is common Rho times V 1 is nothing but QQ is Rho I’m sorry Q is a into V so alien to V is nothing but Q so Q cancels out along with AV 1 so you remain with so the hydraulic efficiency for transistor 1 is Bill W 1 u 1 upon G H is the mechanical efficiency the same thing mechanical efficiency is nothing but the power output from the shaft divided by the power develop button or not that is the mechanical efficiency you and once you get the mechanical efficiency in the hydraulic efficiency you can easily get the value of water efficiency so new overall is nothing but power output from the shaft to the power input pulley you there’s one more formula that is a way in which you can relate both all three efficiencies the old efficiency is the product of hydraulic efficiency in the mechanical efficiency soul efficiencies and Radek efficiency two mechanical efficiency so any to you know you can get the third one next is we’ve seen the work done we’ve seen efficiencies of the three mixed is the discharge for this particular turbine Francis turbine the value of this charge is the same formula of cubed is a times velocity but unlike the Pelton wheel where you had cross section area yo you don’t have cross section you know the flow enters through sides through the circumference to the value of area changes discharge for Francis turbine has a bit different formula so as you can see I’ve drawn a ring kind of a structure and the discharge is not true the top it is two sides so it discharges from sides so you should know the area of the side through which the water is getting in and the width of the runner is known the diameter is known so the area through which the water gets in is nothing but circumference times the width so PI D into B gives you the area through which the water gets in once you know the area you know the velocity of the jet you can get the discharge of multiplying it [Music] so this is the formula for a discharge so you cannot you use the cross section area since the water is not getting in through the cross section it is getting into sides so you should know the area of the side through it the water get it’s in and once I get the area and multiplied with velocity I get addition so this is how you calculate discharge influences to avoid and we already see in the formulas for hydraulic efficiency mechanical efficiency in the overall efficiency so that was all about this topic next we’ll see the numericals on this

sir what will be the work done formula for kaplon turbine as it's inlet velocity angle is 90 degree ?

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You are not showing vector directions for blad velocity at outlet.

bad explanation worst video

squidward meme