Physics Question: Laminar flow?
A paramedic treats an accident victim lying on the ground, transfusing her with a saline solution that has a coefficient of viscosity of η = 1.002 mPa·s, and a density of 1025 kg/m3. The flexible plastic pouch containing the saline solution is 1.85 m above the patient's arm, the needle through which the fluid is being transfused has an inside radius of 0.15 mm and a length of 1.90 cm, and the average gauge pressure of the blood in the patient's vein is 1.33×104 Pa. (a) What is the average volume flow rate of the saline solution into the patient? (b) If this flow rate is too low, what is the first adjustment a paramedic is likely to make in the transfusion apparatus?
a. = ?? m3/s
1. Replace the needle with a shorter one
2. Use a needle with a larger diameter
3. Raise the height of the saline bag
- jeffreyLv 71 decade agoFavorite Answer
The total mass flux dM/dT (the fluid mass flowing through a pipe per unit time) is
(1) ..... dM/dT = * π * (R^4) * ΔP / [ 8 * η * L )
[ see “Physics”, Vol. 1, 4th ed., Resnick/Halliday/Krane, p.408, eq.(20) ]
where = density of fluid , R = radius of pipe , ΔP = pressure difference ,
η = viscosity of fluid , and L = length of pipe.
If we denote by VFR the volume flow rate through the pipe, then
(2) ..... dM/dT = * VFR
Equating the two expressions in (1) and (2), the density cancels out, yielding
(3) ..... VFR = π * (R^4) * ΔP / [ 8 * η * L )
Applied to this problem, the fluid refers to the saline solution being transfused
to the patient while the pipe through which the fluid flows is the needle
through which the fluid is being squeezed into the patient’s vein. The
pressure difference ΔP therefore refers to the pressure at the bottom
of the catheter tube and the pressure in the blood of the patient’s vein.
Given the gauge pressure Pb = 1.33(e+04) Pa in the blood, the pressure
difference is given by
(4) ..... ΔP = * g * H - Pb
where H = 1.85 m is the height of the plastic pouch containing the saline
solution. Substituting the values, we get
.......... VFR = 5.5(e-08) (m^3)/s = [ 5.5(e-08) (m^3)/s ] *[ 1.0(e+06) (cm^3)/ (m^3) ]
(5) ..... VFR = 5.5(e-02) (cm^3)/s = 0.055 (cm^3)/s
which is somewhat too low. In this case, the first adjustment the paramedic is likely
to make in the transfusion apparatus is to raise the height of the saline bag in other
to increase the pressure difference ΔP.
- heckartLv 44 years ago
circulation lined or laminar bypass of liquid by way of a tube would be cutting-edge purely while the speed of a particle at a particular element in any respect cases is an identical. the speed of the debris at diverse factors may well be diverse. It would not rely. the main extreme element is the speed at a particular element continues to be an identical for ever. So any particle arriving that distinctive element could have that velocity meant for that area. So if a colored liquid in few drops is blended alongside with the flowing liquid then we are in a position to visualize the colored strains so fantastically displayed. yet in case of turbulent bypass, no such orderliness. to return to a type the character of bypass Reynold's quantity is sensible that's given as N = rho V D / eta. rho - density of the fluid, V velocity, D diameter of the tube and eta- coefficient of viscosity of the fluid. If N is under 2000, the bypass would be streamlined and if N is extra effective than 3000, actually it particularly is turbulent.
- Anonymous4 years ago
flow coated or laminar flow of liquid with the aid of a tube would be cutting-edge in basic terms while the speed of a particle at a undeniable component in any respect cases is a similar. the speed of the debris at distinctive factors could be distinctive. It would not rely. the main obligatory component is the speed at a undeniable component continues to be a similar for ever. So any particle arriving that distinctive component could have that speed meant for that region. So if a colored liquid in few drops is blended alongside with the flowing liquid then we are in a position to visualize the colored lines so superbly displayed. yet in case of turbulent flow, no such orderliness. to confirm the character of flow Reynold's quantity is useful it relatively is given as N = rho V D / eta. rho - density of the fluid, V speed, D diameter of the tube and eta- coefficient of viscosity of the fluid. If N is under 2000, the flow would be streamlined and if N is extra advantageous than 3000, actual it relatively is turbulent.