Test Calculations - Results Sem01

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Bethany Hill
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1 Test Calculations - Results Sem0 ) Perform unit recalculation: ) 6 km/h? m/s ) d? s 3) Systolic/Diastolic pressure (0/90)? hpa 4) kcal/min? W mm Hg ~33 Pa cal 4.84 J. 6 km/h 6000/3600 m/s.67 m/s.7 m/s. d 4*60*60 s s 3. Systolic/Diastolic pressure (0/90) mmhg (0*33/90*33) Pa ~(60/0) hpa 4. kcal/min (000/60) cal/s (000/60)*4.84 J/s (484/60) W 69.7 W 70 W Remark: Atmospheric pressure 000 hpa 0 5 Pa 00 kpa 0. MPa

2 ) Write using power of 0 and scientific notation: Value Power of 0 Scientific (prefix) Hz 3.5*0 6 Hz 3.5 MHz 0.04 m.4*0 - m.4 cm s.3*0-6 s.3 µs W 6.5*0-3 W 6.5 mw 4000 Pa.4*0 4 Pa 40 hpa 4 kpa

3 3) Calculate the parameters given below: M mass of the body (kg)... H height of the body (m)... Parameter Basal metabolic rate (W) 4.*M 0.75 BSA (m ) 0.0*[M 0.45 ]*[H 0.75 ] VC - Blood volume (L) M/3 Body mass index (BMI) M/[H ] Men: fat (% of M).8*BMI - 0. Women: fat (% of M).48*BMI Value Body mass index (BMI) dimensionless parameter < 8.5 underweight (8.5 5) normal (5 30) overweight > 30 obesity Fat content recommended values Men: fat 7.5 % of the body weight Women: fat 5.0 % of the body weight 3

4 4) Please calculate DC electric current through the human body. outputs of the 30 V power supply are connected to the right and left hands. Assume skin resistance 50 kω and the resistance of the inner part of the body 50 Ω. Ohm s law V R*I R *(skin) + (inner part of the body) R *50 kω + 50 Ω k Ω 00 k Ω V 30 V I 30/(00*0 3 ) V/Ω.3*0-3 A.3 ma Remark: tcdcs trans-cranial Direct Current Stimulation 4

5 5) The area of a rectangle (S) with the sides A and B is calculated using the formula: S A*B. A and B were measured: A 5±0. cm, B 0±0.5 cm. Please calculate the absolute and relative errors of S. y 5 * a * b c m * d n y y a a + n b b + m c c + d d S A*B 5*0 cm 50 cm S S A A + B B S S % 5 0 S 0.09*S 0.09*50 cm 4.5 cm 5

6 Test Calculations Results Sem0 ) Please select all possible isotopes and isobars from the list: H, H, He, 3 H, 3 He, 4 He and select all magnetic nuclei from the list: H, C, 3 C, 6 O, 9 F, 3 P. Isotopes: H, H, 3 H and He, 3 He, 4 He Isobars: H, He and 3 H, 3 He Magnetic moment of a nucleus (µ) Even number of protons and neutrons ( C, 6 O) µ 0 C and 6 O are called non-magnetic nuclei useless in MRI Odd number of protons or neutrons ( H, 3 C, 9 F, 3 P) magnetic nuclei µ 0 H mostly use in MRI 6

7 ) After 5 d the activity of the radioisotope decreases from 30 MBq (initial value) to 0 MBq. Please calculate the halflive time of the radioisotope. The law of radioactive decay N(t) N(0)*exp(-λ λ t) 0 30*exp(-λ*5) exp ln ln(30/0) λ*5 λ /d T / λ T/ 0.693/0.073 d 9.5 d 7

8 3) The package labeling says that a Big Mac contains 5 g of fat, 0 g of carbohydrate and g of protein per 00 g of mass. Please estimate the caloric value of one Big Mac. Average mass of one Big Mac is 0 g. Food or Fuel Net caloric value (kcal/g) Carbohydrates 4. Proteins 4. Fat g fat x 9 kcal/g 35 kcal 0 g of carbohydrate x 4. kcal/g 8 kcal g protein x 4. kcal/g 50.4 kcal 67.4 kcal/00 g Total caloric value.*67.4 kcal 590 kcal 8

9 4) Please calculate the BMR value using the Harris- Benedict equation. Man: BMR *M *H *Y Woman: BMR *M *H *Y [BMR] kcal/d [M] kg body mass 60 kg [H] cm body height 70 cm [Y] y age 5 y Man BMR * * *5 600 kcal/d Woman BMR * * *5 400 kcal/d 9

10 Rounding off general rules Rounding off is the procedure of discarding the insignificant digits and keeping only the significant ones A significant digit is a digit from to 9 or any zero not used to show the position of the decimal point all zeros at the beginning of any number are not the significant digits The following rules are applied ( significant digits): ) number of significant digits does not increase due to calculations ) if the third digit is less than 5 the two first digits are left unchanged and all following digits are dropped or set equal to zero (e.g rounds off to 34) 3) if the third digit is greater than or equal to 5, then the second digit is increased by and all following digits are dropped or set equal to zero (e.g rounds off to 38) The rules presented above for rounding off to two significant digits apply in the same fashion when rounding off to any other number of significant digits BMR Data (mass, age) and 3 (height) significant digits Result significant digits not more than 3 0

11 5) How much does the femur shorten when you stand on two feet? Please assume length of the femur L 0.5 m, cross-sectional area A 370 mm, body mass 70 kg, Young s modulus E 7.9 GPa. Hooke s law σ E*ε Body weight W m*g 70*9.8 N 700 N A 370 mm 370*0-6 m Stress σ W/A 700/(370*0-6 ) N/m.8 MPa Hooke s law σ(stress) E*ε(strain) ε σ/e (.8/7.9) * % The compression of the femur x ε*l (0.*0-3 )*0.5 m 50*0-6 m 50 µm Corrections: For feet x 5 µm Body mass above the hips /3 total mass mabove /3 mtotal x 7 µm

12 Test Calculations Results Sem03 ) Please estimate time which is necessary to transfer oxygen by diffusion (D 0.78 cm /s) from the lung into the blood capillaries. Geometry of the alveolar sac and blood capillary The mean square displacement <r > 6*D*t r 00 µm 00*0-6 m 00*0-4 cm 0 - cm t r 6D * 0.78 cm cm /s ~ 0-4 s Remark: The transit time of the red blood cells through a capillary is ~0.5 s Remark: Anatomy of the human lungs

13 ) Please calculate the compression of air during forced expiration. The maximum alveolar pressure is 30 mmhg. Boyle's law p*v constant pv pv Atmospheric pressure 760 mm Hg V air volume in lungs at the end of inspiration V air volume in lungs at the onset of expiration 760*V ( )*V 790*V 790*(V - V) Compression V/V 760/790 - V/V V/V - 760/ % Changes of air volume (compression) 4% 3

14 3) Please calculate the osmotic pressure of the.0% NaCl solution at 30 K (MNa 3, MCl 35.5). Express the result in Pa and osmol/l. Van t Hoff law of osmotic pressure (π) π c*r*t c concentration (mol/l), T absolute temperature (K), R molar gas constant 8.3 J/mol*K, [π] kpa NaCl Na + + Cl - ions NaCl (.0%) 0 g/l M osmolarity [osmol/l] c*(no ions) 0.34 [osmol/l] T 30 K, R 8.3 J/mol*K π crt*(no ions) 0.7*8.3*30* 88 kpa Pa 9*(atmospheric pressure) Remark: Isotonic solution 0.9% NaCl osmolarity [osmol/l] 4

15 4) Consider a case where is a focal stenosis of a 6 mm diameter femoral artery in which its cross-sectional diameter is reduced to /3 of normal. The velocity at the stenosis, V will be 9 times the upstream velocity V. The volume flow rate is 50 ml/min, the pressure at the upstream, p is 00 mmhg and the blood density ρ.06 g/cm 3. Unit recalculation factor mmhg 33 Pa 330 g/(cm*s ). Please calculate the pressure at the stenosis, p. Volume flow rate Q A*v v Q/A Q 50 ml/min 50/60 ml/s 5/6 ml/s A π(0.6) /4 cm 0.8 cm v Q/A.95 cm/s v 9*v 6.5 cm/s Bernoulli s equation p (.06/)*((6.5) (.95) ) mmhg p p - p mmhg 99.7 mmhg 5

16 5) An intravenous infusion is made under gravity. If the fluid to be delivered has a density.0 g/cm 3, at what height above the vein h should be top surface of the fluid bottle be positioned so the fluid just barely enters the vein? The gauge pressure in the vein is 8 mmhg (Hg density ρhg 3.6 g/cm 3 ). Why is such infusion performed intravenously and not intra-arterially? Hg density ρhg 3.6 g/cm 3 Hydrostatic pressure > Intravenous pressure mm Hg 3.6 mm infusion fluid Hydrostatic pressure > 8 mm Hg 8*3.6 mm infusion fluid 4.5 cm infusion fluid h 4.5 cm Arterial pressure 0 mm Hg h 63 cm 6

17 Test Calculations - Results Sem04 ) Please sketch an electric model to explain the experiment. The patient is connected to earth through a cable with a resistance of R 0 kω (sole of the shoe). Impedance ZC ω * C π * ν * C C 3 pf 3*0 - F, ν 50 Hz π*ν*c *3.4*50*3*0 - (/s)*(c/v) 950*0 - A/V 9.5*0-0 /Ω 0-9 /Ω ZC ~*0 9 Ω Total resistance ZC + R ( ) Ω 0 9 Ω ZC Ohm s law U I*ZC I U/ZC.3*0 /0 9 A 0.3 µa Connected to earth through a resistance of 0 kω 7

18 UBody (~0.3 µa)*(0 kω) ~.3 mv 8

19 ) A defibrillator is a device that applies a strong electric shock to the chest over a time interval of a few ms. Assume that the defibrillator produces an initial current of 00 A which then decay in time ms. The resistance of the body is 00 Ω. Please calculate capacitance of the storage capacitor and the energy deposited in the body by a single discharge of the defibrillator. The potential energy stored in the capacitor EP 0.5*Q*U Ohm s law U I*R 00*00 A*Ω 0 4 V C Q U I*t I*R t R ms 00 Ω 0-5 s Ω 0 μf EP 0.5*Q*U 0.5*C*U J coulomb*volt EP 0.5*0*0-6 *(0 4 ) F*V 500 J 9

20 3) It is well know that the skin resistance varies with the state of sweat glands in the skin (flow of AC current stimulate activity). In an experiment a current of 00 ma at a frequency of 00 khz is passed along a human arm. It is found that the resistance of the arm appears to fall with time. Please explain this observation. Resistance water content Tissue drying coagulation carbonization The skin resistance varies with the state of sweat glands in the skin flow of AC current stimulate activity Sweat gland activity also increases skin resistance decreases Skin resistance can be a measure of emotional and sympathetic responses. 0

21 4) Please calculate the rate at which electric energy is lost at the human skin (electric power - P). Calculate the electric power for the two situations, wet skin (resistance - R kω) and very dry skin (R 500 kω). Assume that the electric potential equals to 40 V. P I*U [P] W A*V U R*I I U/R P U /R R *(skin) + (inner part of the body) R(skin) ~ kω (wet), ~500 kω (very dry), R(inner part of the body) 50 Ω U 40 V IWet 40/( ) 0.06 A Power at the wet skin U*I 4 W IDry 40/(0.5* *0 6 ).4*0-4 A Power at the dry skin 0.06 W After short time (wet skin) skin carbonization R(skin) 0 Ω current ~4.8 A power deposition ~. kw Additional effect AC frequency < ~ khz Heart fibrillation most people who die from electric shock die from fibrillation ~00 ma Muscle contraction let go effect ~0 ma Sensory nerve stimulation ~5 ma Additional effect AC high frequency no effect Perception limit ~ ma

22 5) Trans-cranial direct current stimulation (tdcs) works by sending a low direct current through the electrodes localized at the skull. Depending on electrode polarization the current either increases or decreases neuronal excitability. Please explain why close to the positively charged electrode an increase of the neuronal excitability is observed. Positively charged electrode (anode) concentrations of negative ions increases close to the electrode the resting potential decreases easer to induce neuronal excitability

23 Test Calculations Results Sem05 ) Please calculate the total focusing power of the human eye. What happens when you swim in water (nwater.33)? Lens immersed in a material medium R > 0 R < 0 Focal length of the lens n n n n L - L F R R P focusing power R and R are the curvatures of the first and second surfaces, respectively Part of the Eye n Air.00 Cornea.39 Aqueous humor.35 Lens centre.43 Vitreous humor.35 Cornea R m and R m Lens R 0.0 m and R m 3

24 Cornea P C Lens n L n R n - n R L D m D 43 D m 8 n n n n 4 P L - L D R R m D L m The total focusing power of the eye P PC + PL 43 D +.3 D 64.3 D 64 D.3 D Eye in water The refractive power of the air/cornea interface changes P W C P W C n L n R m 7.5 D 7.5 D D.5 D The total focusing power of the eye in water P W PC + PL.5 D +.3 D.8 D 3 D 4

25 Remark: The eye sees in water very blurred images because the focused image would be beyond the retina ) The sound generator is localized 45 0 to the right from the sagittal cross-section of the head. About how longer will it take for sound (c 330 m/s) to reach left ear than right ear? Distance between right and left ears D is 5 cm while the distance to the sound generator >> D. T D * sin Θ velocity 0.5 * sin 0( ) s 0.5 * s 3.*0-4 s T 0.3 ms 5

26 3) Please consider the ear canal as a resonant cavity and calculate the frequency of the first harmonic. L length of the tube ~8 mm ~0.08 m c velocity of sound in air 330 m/s νn (n - )*c/4*l ν ( - )*c/4*l c/4*l 330/4*0.08 Hz 950 Hz 3 khz H Remark: Resonant frequency ~3 khz the sensitivity of the ear is the best for this frequency 6

27 4) Please calculate the transmission and reflection of the energy as a mechanical wave passes through the air/water interference T - R R (Z (Z + Z Z ) ) Substance Z (kg/s*m ) Air 4.3*0 Water.4*0 6 (Z Z ) (4.3 * 0 R + + (Z Z) (4.3 * * 0 ) 6.4 * 0 ) T - R Remark: Main task of the middle ear is impedance-matching of airfilled ear canal and fluid-filled inner ear without impedance-matching much of the energy of the sound wave would be reflected back out of the ear 7

28 5) A sound generator A, working separately, produces a signal which intensity level at point X is 0 db. A sound generator B, working separately, produces identical signal at point X. Please determine the signal intensity level (in decibels) at point X when generators A and B work together. I Sound intensity level (db) 0* log( ) I The reference sound intensity I is the threshold of perception I 0 - W/m I Sound intensity level A 0* log( ) 0 db I I Sound intensity level B 0* log( ) 0 db I * I Sound intensity level (A + B) 0* log( ) I I 0*log() + 0* log( ) 0* db I 8

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