Explanation Write the expression to calculate the density ( ρ ) of the blood. ρ = S G ρ water (I) Here, the specific gravity of blood is S G . Substitute 1.94 slug/ft 3 for ρ water and 1.06 for S G in Equation (I) ρ = ( 1.06 ) ( 1.94 slug/ft 3 ) = 2.0564 slug/ft 3 Using continuity equation between pipe and needle calculate the velocity of blood in pipe. A 1 V 1 = A 2 V 2 π 4 d 1 2 V 1 = π 4 d 2 2 V 2 V 1 = d 2 2 V 2 d 1 2 (II) Here, the subscript 1, 2 represents to the properties of pipe and needle respectively, velocity is V , area is A Substitute ( 1 8 in . ) for d 1 and ( 1 16 in . ) for d 2 in Equation (II). V 1 = ( 1 16 in . ) 2 V 2 ( 1 8 in . ) 2 V 1 = ( 1 16 in . × 1 ft 12 in . ) 2 V 2 ( 1 8 in . × 1 ft 12 in . ) 2 V 1 = V 2 4 (III) Assume the flow of blood is laminar, write the expression for friction factor ( f ) . f = 64 Re = 64 ρ V D μ = 64 μ ρ V D Write the expression to calculate the major head losses ( h L , major ) . h major = ( f l V 2 ) 2 + ( f l V 2 ) 1 2 g ( D 2 2 + D 1 2 ) (IV) Since, f = 64 μ ρ V D Substitute 64 μ ρ V D for f in Equation (IV). h major = ( 64 μ ρ V D × l V 2 ) 2 + ( 64 μ ρ V D × l V 2 ) 1 2 g ( D 2 2 + D 1 2 ) = ( 64 μ l V 2 ρ g D 2 ) 2 + ( 64 μ l V 2 ρ g D 2 ) 1 = ( 32 μ l V ρ g D 2 ) 2 + ( 32 μ l V ρ g D 2 ) 1 (V) Here, length is l , dynamic viscosity is μ , acceleration due to gravity g , the diameter of the syringe and pipe is D . Substitute 1 × 10 − 4 Ib ⋅ s / ft 2 for μ , V 2 4 for V 1 , ( 1 8 in . ) for d 1 , ( 1 16 in . ) for d 2 , 2 in . for l 2 , 4 ft for l 1 , 2.0564 slug/ft 3 for ρ , 32.2 ft/s 2 for g in Equation (V). h major = { ( 32 ( 1 × 10 − 4 Ib ⋅ s / ft 2 ) ( 2 in . × 1 12 ft ) V ( 2.0564 slug/ft 3 ) ( 32.2 ft/s 2 ) ( 1 16 in . × 1 12 ft ) 2 ) 2 + ( 32 ( 1 × 10 − 4 Ib ⋅ s / ft 2 ) ( 4 ft ) ( V 2 4 ) ( 2.0564 slug/ft 3 ) ( 32.2 ft/s 2 ) ( 1 8 in . × 1 12 ft ) 2 ) 1 } = 0.2969 V 2 ft + 0.4453 V 2 ft = 0.7422 ( V 2 ) ft = 0.7422 ( V 2 ) n o z z l e ft Write the expression to calculate the minor losses h L , minor . h minor = ( K entrance V 2 + K exit V 2 2 g ) 2 + ( K entrance V 2 + K exit V 2 2 g ) 1 (V) Here, the subscripts 1 and 2 stands for variables of pipe and nozzle respectively, the loss coefficient at the entrance is K entrance and the loss coefficient at the exit is K e x i t

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ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condit…

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The time required ( t ) for the person to donate one pint of blood.

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