A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus inside the capillary in time $t$ is given by $L = k \gamma^a R^b \mu^c \sqrt{t},$ where $ \gamma $ is the surface tension, $ R $ is the inner radius of the capillary, and $ \mu $ is the dynamic viscosity of the liquid. If $ k $ is a dimensionless constant, then the exponent $ a $ is _______ (rounded off to 1 decimal place).

GATE 2024 Mechanical Engineering PYQ — Fluid Mechanics

GATE 20242024PYQNATanswer pendingexplanationmedium

Fluid Mechanics · Fluid Properties

Concept intelligence

Drill mode: dimensional analysis · 3/5

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Recurring concept

Fluid Properties has appeared in GATE Mechanical Engineering 16 times across 12 years (2008, 2010, 2014, 2016, 2024, ...).