Chapter 7 Flashcards
Horizontal force (Rx) on a stationary plate at an angle theta (§)?
Rx = p * a1 * V1 * ( V1 * Cos(§) - 0) Rx = p * a1 * V1^2 * Cos(§)
p = density of water a1 = C-S area of the jet § = theta (angle to the horizontal)
Horizontal and Vertical forces (Rx & Ry) on a curved plate? Hence find resultant force and the angle it’s moving in.
Rx = p * a1 * V1 * ( V1 -Vxout)
Ry = p * a1 * V1 * ( 0 - Vyout)
R = sqt( Rx^2 + Ry^2 )
tan(§) = Ry / Rx
If a flat plate perpendicular to the jet stream is moving at a speed of u, how do you find the force on the plate?
And how do you find the power on the plate?
For a flat plate, how does the plate velocity and jet velocity relate?
you need to find the relative momentum of the plate.
Rx = Mr * ( Vin - Vout)
Rx = p * a1 * ( V1 - u) * ( (v1-u) - 0)
Power = R * u
u = V / 3
Whats is the difference between impulse and reaction turbines? Give examples.
Impulse turbines use the momentum of a jet stream of water hitting a plate to turn the turbine and store energy.
Pelton wheel developed in the 1880s.
Whereas, reaction turbines are completely filled with water and under significant pressure. The energy extracted from the pressure difference on one side to the other.
The Francis turbine
The Kaplan turbine
Name the 4 types of pumps.
Reciprocating pumps
Centrifugal pumps
Axial Flow-Screw pump
Mixed flow
Describe the two types of reciprocating pumps:
Bucket pump: operates vertically to draw water from a well
Ram pump: Piston reciprocates within a cylinder, water is sucked in by one stroke and forced out by the next.
With a single ram, the outputs vary.
Tripple throw ram-pistons connected 120 degrees apart give approximately constant flow.
Slow speed
High heads achievable
useful if solids are in liquid
Describe what centrifugal pump does and what the two types are:
Flow enters at the centre then is accelerated outwards by the impeller blades, and leaves the outer edge at higher flow rates and/or pressures.
Single-stage: moderate flow with a high head. Robust and generally used for continuous heavy-duty.
Multi-stage: several impellers and diffuser chambers clamped together in series with impellers fixed to one shaft. Increases the head at the output pump.
Describe Axial Flow-Screw Pumps and mixed flow pumps:
Axial Flow-Screw pumps: Consists of a propeller (axial impeller) inside a pipe. Large flows against low heads.
Mixed flow: a combination of centrifugal and axial blades given some degree of twist. The impellers force the water one direction until it reaches the edge. Then the water stops and compresses to make higher pressure. Moving the other way, the water is forced out.
Does the velocity change going into the pump as leaving?
No
Power of the pump = ?
Power = p * g * Q * Ht
p =. rho
Ht =. theoretical head of the pump
Euler pump/ Turbine equation
Ht = ?
What if the incoming flow was completely normal to the rotation?
Ht = 1/g * ( u2*V2*Cos(§2) - u1*V1*Cos(§1) ) § = angle in tangential triangle with angle § and B u = tangential instantaneous velocity.
Ht= ( u2 * V2 * Cos(§2) ) / g
Substituting angular velocity into the Euler pump/ Turbine equation:
Ht = ( w^2 * r2^2) / g - ( wCos(B2) * Q ) / (2pib2g)
The difference between the theoretical pump curve and real pump curve?
Give reasons:
The theoretical pump curve is straight and always higher than the real pump curve.
The real pump curve is a sloped down as the flowrate gets higher.
-pre-rotation of fluid before it enters the impellers ie §1 doesn’t = 90
-flow separations due to imperfect guidance of fluid.
-flow separation in the housing
-cavitation in the pump, when the pressure drops to the fluid vapour pressure.
-flow leakage, flow passes backwards through the pump.
Axial flow pumps:
Ht = ?
Ht = u^2 / g - (uVncot(B2)) / g
Pump efficiency (n) = ?
n = Wf / Wp = (pgQH) / (wT)
Wf = the power applied to a fluid as measured Wp = the power applied to the impeller.
