Advertisements
Advertisements
प्रश्न
(a) What is the largest average velocity of blood flow in an artery of radius 2 × 10–3 m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10–3 Pa s).
Advertisements
उत्तर १
a)
Radius of the artery, r = 2 × 10–3 m
Diameter of the artery, d = 2 × 2 × 10–3 m = 4 × 10– 3 m
Viscosity of blood, eta = `2.084 xx 10^(-3)` Pas
Density of blood, ρ = 1.06 × 103 kg/m3
Reynolds’ number for laminar flow, NR = 2000
The largest average velocity of blood is given by the relation:
`V_"arg" = (N_Reta)/(rhod)`
= `(2000xx2.084xx10^(-3))/(1.06xx10^3xx4xx10^(-3))`
= 0.983 m/s
Therefore, the largest average velocity of blood is 0.983 m/s.
b) Flow rate is given by the relation:
`R = pir^2V_"arg"`
`= 3.14 xx (2xx10^(-3))^2 xx 0.983`
`= 1.235 xx 10^(-5) m^3 s^(-1)`
Therefore, the corresponding flow rate is `1.235 xx 10^(-5) m^3 s^(-1)`
उत्तर २
Here `r = 2 xx 10^(-3) m; D = 2r = 2xx2xx10^(-3) = 4xx 10^(-3) m`
`eta = 2.084 xx 10^(-3) Pa-s; rho = 1.06 xx 10^3 kg m^(-3)`
For flow to be laminar , `N_R = 2000`
a) Now `v_c = `(N_Reta)/rho_D` = (2000xx(2.084xx10^(-3)))/((1.06xx10^3)xx(4xx10^(-3))) = 0.98 "m/s"`
b)Volume flowering per second =`pir^2v_c = 22/7 xx (2xx10^(-3))^2 xx 0.98 = 1.23 xx 10^(-5) m^3s^(-1)`
संबंधित प्रश्न
Fill in the blanks using the word(s) from the list appended with each statement
Viscosity of gases. .. with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
Fill in the blanks using the word(s) from the list appended with each statement
For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for fluids it is proportional to . .. (shear strain / rate of shear strain)
Explain why The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
The viscous force acting between two layers of a liquid is given by \[\frac{F}{A} = - \eta\frac{dv}{dz}\]. This F/A may be called
Which has greater viscosity, oil or honey? Why?
A small sphere of radius 2 cm falls from rest in a viscous liquid. Heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to
In a horizontal pipe of non-uniform cross-section, water flows with a velocity of 1 ms−1 at a point where the diameter of the pipe is 20 cm. The velocity of water (1.5 ms−1) at a point where the diameter of the pipe is (in cm)
Define the coefficient of viscosity of a liquid.
Two streamlines cannot cross each other. Why?
A block of Ag of mass x kg hanging from a string is immersed in a liquid of relative density 0.72. If the relative density of Ag is 10 and tension in the string is 37.12 N then compute the mass of Ag block.
A small metal sphere of mass M and density d1, when dropped in a jar filled with liquid moves with terminal velocity after sometime. The viscous force acting on the sphere is (d2 = density of liquid and g = gravitational acceleration)
Choose the CORRECT statement.
The tangential force or viscous drag on any layer of the liquid is directly proportional to the velocity gradient `"dv"/"dx"`. Then the direction of dx velocity gradient is ____________.
An air bubble of negligible weight having radius r rises steadily through a solution of density σ at speed v. The coefficient of viscosity of the solution is given by ______.
A liquid of density ρ and coefficient of viscosity η flows with velocity v through a tube of diameter D. A quantity `"R" = (rho"vD")/η`, determines whether the flow will be streamlined or turbulent. R has the dimension of ______.
An incompressible liquid is flowing through a uniform cross-sectional tube with a velocity 12 cm/ s. If the thickness of liquid layer is 0.8 cm, what is the velocity gradient of that flow of liquid?
State and explain Newton's law of viscosity.
The dimensions of coefficient of viscosity are ______.
