APPLIED FLUID MECHANICS

Syllabus covered (by AT) Module 1: Specific energy, Hydraulic Jump. Module 2: Compressible Flow: speed of propagation of a small disturbance through a compressible fluid, sonic velocity, Mach number, mach cone and Mach wave; isentropic flow, stagnation properties of a compressible flow, isentropic pressure, temperature and density ratios; compressibility correction factor in the measurement of air speed; area – velocity relationship for compressible flow through a variable area duct, mass flow rate through a duct, critical condition and choking; flow through convergent-divergent nozzle. Module 3: Ideal Fluid Flow: rotation of a fluid particle, vorticity, rotational and irrotational motion; velocity potential function, circulation, stream function, flownet; governing equation for two dimensional irrotational motion, simple two dimensional irrotational flows like uniform flow, plane source, plane sink etc; superimposition of simple irrotational flows, combination of a source and a sink.

Syllabus covered (by SG) Module 4: Analysis of flow through propellers and windmills – slip stream theory, actuated disc theory; jet propulsion devices – analysis of thrust and other performance parameters. Module 5: Similarity and model study in turbomachines: dimensional analysis of incompressible flow turbomachines, flow coefficient, head coefficient and power coefficient; non-dimensional plot of performance curves; specific speed; Cordier diagram; specific speed as a design parameter of imcompressible flow turbomachines; unit quantities for hydroturbines. Module 6: Mechanical, hydraulic and volumetric loss in a turbo-pump; different types of losses in a hydroturbine installation; different efficiencies in turbomachines.

Syllabus covered (by SG) Module 7: Interaction of a turbomachine with the pipeline system; system head curve and point of operation, surging, series and parallel operation of pumps and fans. Module 8: Testing of hydroturbines, different performance characteristics of hydroturbines like operating characteristics, main characteristics, Muschel curves; speed governing of hydroturbines – different methods. Module 9: Torque converter and fluid coupling – function and performance.

PHYSICAL PHENOMENON IN HYDRAULIC MACHINE 𝑓 𝑸,𝒈𝑯, 𝑷,𝑫, 𝒍 𝒊 , 𝜺, 𝑵, 𝝁, 𝝆 =0 Applying Buckingham -theorem considering Repeating variable as D, N,  𝝅 𝟏 =𝑸 𝑫 𝒂 𝟏 𝑵 𝒃 𝟏 𝝆 𝒄 𝟏  𝑸 𝑵 𝑫 𝟑 Flow Coefficient 𝝅 𝟐 =𝒈𝑯 𝑫 𝒂 𝟐 𝑵 𝒃 𝟐 𝝆 𝒄 𝟐  𝒈𝑯 𝑵 𝟐 𝑫 𝟐 Head Coefficient 𝝅 𝟑 =𝑷 𝑫 𝒂 𝟑 𝑵 𝒃 𝟑 𝝆 𝒄 𝟑  𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 Power Coefficient 𝝅 𝟒 =µ 𝑫 𝒂 𝟒 𝑵 𝒃 𝟒 𝝆 𝒄 𝟒  µ 𝝆𝑵 𝑫 𝟐 𝝅 𝟓 =𝜺 𝑫 𝒂 𝟓 𝑵 𝒃 𝟓 𝝆 𝒄 𝟓  𝜺 𝑫 Relative Roughness 𝝅 𝒊 = 𝒍 𝒊 𝑫 𝒂 𝒊 𝑵 𝒃 𝒊 𝝆 𝒄 𝒊  𝒍 𝒊 𝑫

PHYSICAL IMPORTANCE OF  TERMS 𝝅 𝟏 = 𝑸 𝑵 𝑫 𝟑 𝝅 𝟐 = 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝝅 𝟑 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝝅 𝟒 = µ 𝝆𝑵 𝑫 𝟐 𝝅 𝟏 = 𝑸 𝑵 𝑫 𝟑 = 𝑸 𝑫 𝟐 𝑵𝑫  𝒄𝒉𝒂𝒓𝒂𝒄𝒕𝒆𝒓𝒊𝒔𝒕𝒊𝒄 𝒇𝒍𝒖𝒊𝒅 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 (𝑽) 𝑪𝒉𝒂𝒓𝒂𝒄𝒕𝒆𝒓𝒊𝒔𝒕𝒊𝒄 𝒓𝒐𝒕𝒐𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 (𝒖) 𝝅 𝟐 𝝅 𝟏 𝟐 = 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝑵 𝟐 𝑫 𝟐 𝑸 𝑫 𝟐 𝟐 = 𝒈𝑯 𝑸 𝑫 𝟐 𝟐  𝑭𝒍𝒖𝒊𝒅 𝒆𝒏𝒆𝒓𝒈𝒚 𝒔𝒕𝒐𝒓𝒆𝒅 𝑲𝒊𝒏𝒆𝒕𝒊𝒄 𝑬𝒏𝒆𝒓𝒈𝒚 𝝅 𝟑 𝝅 𝟐 𝝅 𝟏 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝑵 𝑫 𝟑 𝑸 𝑵 𝟐 𝑫 𝟐 𝒈𝑯 = 𝑷 𝝆𝒈𝑸𝑯 =  𝒐 𝒊𝒏 𝒄𝒂𝒔𝒆 𝒐𝒇 𝒕𝒖𝒓𝒃𝒊𝒏𝒆 = 𝟏  𝒐 (𝒊𝒏 𝒄𝒂𝒔𝒆 𝒐𝒇 𝒑𝒖𝒎𝒑) 𝝅 𝟒 𝝅 𝟏 = µ 𝝆 𝑵𝑫 𝑫 𝑵𝑫 𝑸 𝑫 𝟐 = µ 𝝆 𝑸/ 𝑫 𝟐 𝑫 = 𝟏 𝑹𝒆𝒚𝒏𝒐𝒍𝒅 𝒔 ′ 𝑵𝒐 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒇𝒍𝒖𝒊𝒅 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚

HOMOLOGUS SERIES 𝝅 𝟏 = 𝑸 𝑵 𝑫 𝟑 𝝅 𝟐 = 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝝅 𝟑 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝝅 𝟐 = 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝝅 𝟑 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝝅 𝟒 = µ 𝝆𝑵 𝑫 𝟐 𝑭 𝑸 𝑵 𝑫 𝟑 , 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 , 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 , µ 𝝆𝑵 𝑫 𝟐 =𝟎 𝑭 𝑸 𝑵 𝑫 𝟑 , 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 , 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 =𝟎 FOR TURBINE 𝝅 𝟔 = 𝝅 𝟑 𝟏 𝟐 𝝅 𝟐 𝟓 𝟒 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝟏 𝟐 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝟓 𝟒 = 𝑵 𝑷 𝟏 𝟐 𝝆 𝟏 𝟐 𝒈𝑯 𝟓 𝟒 𝑵 𝒎 𝑷 𝒎 𝟏 𝟐 𝝆 𝒎 𝟏 𝟐 𝒈 𝒎 𝑯 𝒎 𝟓 𝟒 = 𝑵 𝒑 𝑷 𝒑 𝟏 𝟐 𝝆 𝒑 𝟏 𝟐 𝒈 𝒑 𝑯 𝒑 𝟓 𝟒 Geometrically similar model turbine working under 1m head, will generate 1kW power, if it is rotating at 𝑁 𝑆 𝑇 rpm 𝑵 𝒔 𝑻 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝑺𝒑𝒆𝒆𝒅 = 𝑵 𝑷 𝟏 𝟐 𝑯 𝟓 𝟒 𝑲 𝒔 𝑻 𝑫𝒊𝒎𝒆𝒏𝒔𝒊𝒐𝒏𝒍𝒆𝒔𝒔 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝑺𝒑𝒆𝒆𝒅 = 𝑵 𝑷 𝟏 𝟐 𝝆 𝟏 𝟐 𝒈𝑯 𝟓 𝟒

HOMOLOGUS SERIES 𝝅 𝟏 = 𝑸 𝑵 𝑫 𝟑 𝝅 𝟐 = 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝝅 𝟑 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝝅 𝟐 = 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝝅 𝟑 = 𝑷 𝝆 𝑵 𝟑 𝑫 𝟓 𝝅 𝟒 = µ 𝝆𝑵 𝑫 𝟐 FOR PUMP 𝝅 𝟕 = 𝝅 𝟏 𝟏 𝟐 𝝅 𝟐 𝟑 𝟒 = 𝑸 𝑵 𝑫 𝟑 𝟏 𝟐 𝒈𝑯 𝑵 𝟐 𝑫 𝟐 𝟑 𝟒 = 𝑵 𝑸 𝟏 𝟐 𝒈𝑯 𝟑 𝟒 𝑵 𝒎 𝑸 𝒎 𝟏 𝟐 𝒈 𝒎 𝑯 𝒎 𝟑 𝟒 = 𝑵 𝒑 𝑸 𝒑 𝟏 𝟐 𝒈 𝒑 𝑯 𝒑 𝟑 𝟒 Geometrically similar model Pump working under 1m head, will pump 1m3/sec flow-rate, if it is rotating at 𝑁 𝑆 𝑃 rpm. 𝑵 𝒔 𝑷 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝑺𝒑𝒆𝒆𝒅 = 𝑵 𝑸 𝟏 𝟐 𝑯 𝟑 𝟒 𝑲 𝒔 𝑷 𝑫𝒊𝒎𝒆𝒏𝒔𝒊𝒐𝒏𝒍𝒆𝒔𝒔 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝑺𝒑𝒆𝒆𝒅 = 𝑵 𝑸 𝟏 𝟐 𝒈𝑯 𝟑 𝟒

Problem 1 : A turbine develops 500 kW power under a head of 100 meters at 200 rpm. What should be its normal speed and output under a head of 81 meters?

Problem 2: A radial flow hydraulic turbine is required to be designed to produce 20 MW under a head of 16 m. at a speed of 90 rpm. A geometrically similar model with an output of 30kW and a head of 4m is to be tested under dynamically similar conditions. At what speed must the model be run? What is the required impeller diameter ratio between the model and prototype and What is the volume flow rate through the model if its efficiency can be assumed to be 90%?

NON-DIMENSIONAL PERFORMANCE CURVE

DIMENSIONAL PERFORMANCE CHARACTERISTICS OF CENTRIFUGAL PUMP

HEAD DISCHARGE CURVE (DIMENSIONAL)

HEAD COEFFICIENT AS A FUNCTION OF FLOW COEFFICIENT FOR CENTRIFUGAL PUMP  2000 min-1, Re = 6,81,800  1800 min-1, Re = 6,13,600  1600 min-1, Re = 5,45,500  1400 min-1, Re = 4,77,300  1200 min-1, Re = 4,09,100

EFFICIENCY vs DISCHARGE CURVE (DIMENSIONAL)

EFFICIENCY AS A FUNCTION OF FLOW COEFFICIENT FOR CENTRIFUGAL PUMP  2000 min-1, Re = 6,81,800  1800 min-1, Re = 6,13,600  1600 min-1, Re = 5,45,500  1400 min-1, Re = 4,77,300  1200 min-1, Re = 4,09,100

INPUT POWER vs DISCHARGE CURVE (DIMENSIONAL)

POWER COEFFICIENT AS A FUNCTION OF FLOW COEFFICIENT FOR CENTRIFUGAL PUMP  2000 min-1, Re = 6,81,800  1800 min-1, Re = 6,13,600  1600 min-1, Re = 5,45,500  1400 min-1, Re = 4,77,300  1200 min-1, Re = 4,09,100

UNIT QUANTITIES FOR HYDROTURBINES Unit Speed (Nu) This is the speed of a turbine working under a unit head Unit Power (Pu) This is the Power developed by the turbine working under a unit head Unit Discharge (Qu) This is the discharge through the turbine working under a unit head

CORDIER DIAGRAM

DIFFERENT LOSSES IN PUMPS

Efficiencies in Turbine

Pump Pp (PSh) Pi Pf Pl hl QL

PUMPS IN SERIES System Characteristics Head (H) Pump B Pump A + B in Series Pump A Discharge (Q)

PUMPS IN PARALLEL Head (H) System Characteristics Two Pumps in Series Discharge (Q)

Water is pumped between two reservoirs in a pipeline with the following characteristics : D = 300 mm, L = 70m, f = 0·025, by the formula : HP = (22.9 + 10.7Q – 111 Q2)m where Q is m3/s. Determine the discharge QD and pump head HD for the following situations : (i) z2 - z1 = 15 m, one pump placed in operation (ii) the pump layout, discharge and head for z2 - z1 = 25m. (iii) z2 - z1 = 15 m, with two identical pumps operating in parallel

GOVERNING OF IMPULSE TURBINE

GOVERNING OF REACTION TURBINE