Answer

Verified

436.2k+ views

**Hint:**In this question, we need to determine the individual pressure across the two tubes. For this we will use the relation between the flow rate formulas and find the pressure in the individual tubes.

**Complete step by step answer:**Radius of tube 1 = R

Length of tube 1 = L

Radius of tube 2 =\[\dfrac{R}{2}\]

Length of tube 2=\[\dfrac{L}{8}\]

Let,

The pressure drop across tube 1 is \[{P_1}\]

And the pressure drop across tube 2 is \[{P_2}\]

Hence we can say\[{P_1} + {P_2} = P - - (i)\], since the pressure across the tubes taken together is P

Now we know Flow rate\[ = \dfrac{{\pi \Delta {{\Pr }^4}}}{{8\eta L}}\]

Now since the both tube are in series, hence we can say flow rate will be same for both the pipes so we write

\[

\dfrac{{\pi \Delta {\operatorname{P} _1}{r_A}^4}}{{8\eta {L_A}}} = \dfrac{{\pi \Delta {\operatorname{P} _2}{r_B}^4}}{{8\eta {L_B}}} \\

\dfrac{{\pi \Delta {\operatorname{P} _1}{R^4}}}{{8\eta L}} = \dfrac{{\pi \Delta {\operatorname{P} _2}{{\left( {\dfrac{R}{2}} \right)}^4}}}{{8\eta \dfrac{L}{8}}} \\

\dfrac{{\pi \Delta {\operatorname{P} _1}{R^4}}}{{8\eta L}} = \dfrac{1}{2}\dfrac{{\pi \Delta {\operatorname{P} _2}{R^4}}}{{8\eta L}} \\

2{\operatorname{P} _1} = {\operatorname{P} _2} \\

\]

Where \[{P_1} + {P_2} = P\]from equation (i), now we substitute \[2{\operatorname{P} _1} = {\operatorname{P} _2}\]in this equation to find the pressure across the two tubes separately

\[

{P_1} + 2{P_1} = P \\

3{P_1} = P \\

\therefore {P_1} = \dfrac{P}{3} \\

\]

Hence the pressure in pipe B will be equal to

\[

{\operatorname{P} _2} = 2{\operatorname{P} _1} \\

= 2 \times \dfrac{P}{3} \\

= \dfrac{{2P}}{3} \\

\]

Therefore the pressure in pipe \[{P_1} = \dfrac{P}{3}\] and pipe \[{\operatorname{P} _2} = \dfrac{{2P}}{3}\]respectively

Option D is correct

**Note:**Flow rate is the volume of fluid flowing through an area each second which is given by the formula

\[Q = \dfrac{{\pi \Delta {{\Pr }^4}}}{{8\eta L}}\], where L is the length of tube, r is the radius of the tube, P is the pressure of fluid through the pipe.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The mountain range which stretches from Gujarat in class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths