Engineering, 04.05.2020 22:31 dannyhouseman55

The velocity, c, at which pressure pulses travel through arteries (pulse-wave velocity) is a function of the artery diameter, D, and wall thickness, h, the density of blood, p, and the modulus of elasticity, E, of the arterial wall.

Determine a set of nondimensional parameters that can be used to study experimentally the relationship between the pulse-wave velocity and the variables listed. Form the nondimensional parameters by inspection.

Answers: 2

Show answers

Answers

Answer from: jaymoney0531

$\frac{E}{pc^{2} } =f\frac{h}{D}$

Explanation:

Using the Buckingham pi theorem and following the series of steps below;

STEP 1

List all the variables involved:

Velocity = c

Artery diameter = D

Wall thickness = h

Density = ρ

Modulus of elasticity = E

(c, D, h, ρ, E) = 5 variables

STEP 2

Express each of the above variables in their basic physical dimension (MLT)

c = L $T^{-1}$

D = L

h = L

ρ = M $L^{-3}$

E = M $L^{-1} T^{-2}$

STEP 3

Determine the required number of pi (π) terms using the below formula;

π = n - m

where n = number of dimensional variables = 5

m = number of dimensions the variables are expressed in = 3 (M,L,T)

Therefore, π = 5-3 = 2; π = 2

STEP 4

Select a number of repeating variables, where the number required is equal to the number of dimensions used i.e. 3. The remaining two variables are the non repeating variables.

Selected repeating variables are c, D, ρ

non repeating variables are h and E

STEP 5

Form a pi term by multiplying one non repeating variable by the product of the repeating variables, each (repeating variables) raised to an exponent that will make the expression dimensionless.

π (1) = h $D^{a} c^{b} p^{c}$ ...............................................(i)

express this pi terms in their fundamental dimension and equate it to $M^{0} L^{0} T^{0}$

$M^{0} L^{0} T^{0}$ = $L (L)^{a} (LT^{-1} )^{b} (ML^{-3} )^{c}$

$M^{0} L^{0} T^{0} = M^{c} L^{1+a+b-3c} T^{-b}$

Equate the powers

$c=0\\b=0\\1+a+b-3c =0\\a = -1$

substitute c and b into the third expression to find a

a = -1, b = 0, c = 0

substitute the values for a, b and c in (i)

π (1) = $hD^{-1}$

π (1) = $\frac{h}{D}$

STEP 6

Repeat step 5 for the second non repeating variable E

π (2) = $ED^{a} c^{b} p^{c}$ .......................................................... (ii)

express in fundamental dimensions

$M^{0} L^{0} T^{0} =(ML^{-1}T^{-2}) (L)^{a}(LT^{-1})^{b}(ML^{-3} )^{c}$

$M^{0} L^{0} T^{0} = M^{1+c} L^{-1+a+b-3c} T^{-2-b}$

compare the powers

$1+c=0\\-1+a+b-3c=0\\-2-b=0$

using elimination method,

a = 0, b = -2, c = -1

substituting the values of a, b and c in (ii)

π (2) = $ED^{0} c^{-2} p^{-1}$ = $\frac{E}{pc^{2} }$

π (2) = $\frac{E}{pc^{2} }$

STEP 7

Check if the pi terms are dimensionless

π (1) = $\frac{h}{D}=\frac{L}{L}=M^{0} L^{0} T^{0}$

π (2) = $\frac{E}{pc^{2} } =\frac{ML^{-1} T^{-2} }{ML^{-3} (LT^{-1} )^{2} } =M^{0} L^{0} T^{0}$

STEP 8

Express the final equation as a relationship between the pi terms in the form,

π() = π()

$\frac{h}{D}=f\frac{E}{pc^{2} }\\ or\\\frac{E}{pc^{2} }=f\frac{h}{D}$

Answer from: Quest

Answer:

the answer is d.

explanation:

Answer from: Quest

post office i thinkexplanation:

Other questions on the subject: Engineering

Engineering, 04.07.2019 18:10, koolgurl2003

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Answers: 1

continue

Engineering, 04.07.2019 18:10, meganwintergirl

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

Answers: 3

continue

Engineering, 04.07.2019 18:20, kendrawalraven

The characteristic roots of a dynamic system are: 1.7920 1.8160 i, -1.7920 1.8160 i, -0.4160 what is the order of this system? what are the settling time and damping ratio of the system?

Answers: 3

continue

Engineering, 04.07.2019 19:10, kelseiroll9759

Ahelical coil spring has a mean diameter of 50 mm, a wire diameter of 5.5 mm and is wound with a pitch of 10 mm. the spring steel has an ultimate strength of 1250 mpa. find the force needed to compress the spring solid and the wire stress in this condition. state whether the spring will return to its initial length.

Answers: 1

continue

You know the right answer?

The velocity, c, at which pressure pulses travel through arteries (pulse-wave velocity) is a functio...