Applying a pressure drop across a capillary results in a volumetric flow rate 'Q' under laminar flow conditions. The flow rate for the same pressure drop, in a capillary of the same length but half the radius is
A. $$\frac{{\text{Q}}}{2}$$
B. $$\frac{{\text{Q}}}{4}$$
C. $$\frac{{\text{Q}}}{8}$$
D. $$\frac{{\text{Q}}}{{16}}$$
Answer: Option D
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Comments ( 2 )
A. Thermal conductivity
B. Electrical conductivity
C. Specific gravity
D. Electrical resistivity
A. $$\frac{{\text{V}}}{{{{\text{V}}_{\max }}}} = {\left( {\frac{{\text{x}}}{{\text{r}}}} \right)^{\frac{1}{7}}}$$
B. $$\frac{{\text{V}}}{{{{\text{V}}_{\max }}}} = {\left( {\frac{{\text{r}}}{{\text{x}}}} \right)^{\frac{1}{7}}}$$
C. $$\frac{{\text{V}}}{{{{\text{V}}_{\max }}}} = {\left( {{\text{x}} \times {\text{r}}} \right)^{\frac{1}{7}}}$$
D. None of these
A. d
B. $$\frac{1}{{\text{d}}}$$
C. $$\sigma $$
D. $$\frac{l}{\sigma }$$
A. $$\frac{{4\pi {\text{g}}}}{3}$$
B. $$\frac{{0.01\pi {\text{gH}}}}{4}$$
C. $$\frac{{0.01\pi {\text{gH}}}}{8}$$
D. $$\frac{{0.04\pi {\text{gH}}}}{3}$$
According to Hagen Posuille equation for laminar flow
∆P=32 ulv/d^2. gc
Then , v= ∆P. d^2. gc/32ul...............(1)
We know that the volumetric flow rate given as Q= A.v..........(2)
area for capillary can be given as π/4 d^2
Put the value of v in eqn (2 )
Q= ∆P . d^4.gc/32ul
Q= (d/2)^4
We know that half the radius then ,,,, Q= (r/2)^4
Q= r^4/16
Q=
??