व्यास 'd' की एक ग्लास ट्यूब में, तरल का केशिकीय उत्थान या पतन (h), जहां पृष्ठ का संसंजन σ है, संपर्क का कोण 'θ' है, समीकरण किसके द्वारा दिया जाता है?

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HPCL Engineer (Civil) 04 Nov 2022 Official Paper
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  1. h = w cos θ/d
  2. h = 4 cos θ/d
  3. h = 4 σ cos θ/wd
  4. h = flv/d

Answer (Detailed Solution Below)

Option 3 : h = 4 σ cos θ/wd
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संकल्पना:

पृष्ठ तनाव σ, संपर्क कोण θ, ट्यूब व्यास d, और विशिष्ट भार w को जानकर केशिका ट्यूब में तरल की वृद्धि/कमी का विश्लेषण किया जा सकता है।

द्रव की वृद्धि/कमी का भार  \(\frac{\pi }{4}{d^2}h.w\) है

पृष्ठ तनाव बल का ऊर्ध्वाधर घटक  \(\sigma cosθ \times \pi d\) है

साम्यावस्था के तहत: \(\frac{\pi }{4}{d^2}h.w = \;\sigma cosθ \times \pi d\)

\(h = \frac{{4\sigma cosθ }}{{wd}}= \frac{{2\sigma cosθ }}{{wR}}\)

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