આકૃતિમાં દર્શાવ્યા મુજબ બદલાતા જતા આડછેદના ક્ષેત્રફળવાળી નળીમાંથી આપેલ ધનતા ધરાવતું પ્રવાહી વહન પામે છે. જો \(A\) આડછેદનું ક્ષેત્રફળ \(1.5\,cm ^2\) અને \(B\) નું \(25\,mm ^2\) તથા જો \(B\) આગળ પ્રવાહીની ઝડપ \(60\,cm / s\) હોય. \(\left( P _{ A }- P _{ B }\right)\) ............. \(pa\) થશે. (\(A\) અને \(B\) બિંદુઓ આગળ પ્રવાહીના દબાણ \(P_A\) અને \(P_B\) છે. \(\rho=1000\,kg\,m ^{-3}\) \(A, B\), નળીની અક્ષ પરના બિંદુઓ છે.)

A \(175\)
B \(27\)
C \(135\)
D \(36\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(175\)

Step-by-step Solution

Detailed explanation

From continuity theorem \(A_1 V_1=A_2 V_2\) \(1.5 \times V_1=25 \times 10^{-2} \times 60\) \(V_1=\frac{25 \times 60 \times 10^{-2} \times 10}{1.5}\) \(V_1=10\,cm / s\) By Bernoulli's theorem \(P_1+\frac{1}{2} \times 1000 \times(0.1)^2=P_2+\frac{1}{2} \times 1000 \times(0.6)^2\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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