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Tutorial 3

The tutorial sheet outlines various fluid mechanics problems related to hydrostatic forces, buoyancy, and stability of submerged bodies. Topics include calculating forces on a hemispherical tank bottom, analyzing a concrete dam's tipping angles, deriving relationships between metacentre and centre of buoyancy, and exploring conditions for floating bodies. Additional problems involve pressure calculations in a rotating tube and fluid behavior on an inclined plane under constant acceleration.

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21 views2 pages

Tutorial 3

The tutorial sheet outlines various fluid mechanics problems related to hydrostatic forces, buoyancy, and stability of submerged bodies. Topics include calculating forces on a hemispherical tank bottom, analyzing a concrete dam's tipping angles, deriving relationships between metacentre and centre of buoyancy, and exploring conditions for floating bodies. Additional problems involve pressure calculations in a rotating tube and fluid behavior on an inclined plane under constant acceleration.

Uploaded by

u92485179
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Tutorial Sheet - 3

CLL231, Semester-2, 2024-25

1. An open cylindrical tank contains water and has a hemispherical bottom, as shown in
the diagram. Determine the magnitude, line of action, and direction of the force of the
water on the curved bottom. Determine the expression through integration of force
acting on a point on hemisphere without first taking weight of liquid above it into
consideration. Take the height of liquid from the bottom as h and radius of hemisphere
as R. Use ρ = ρ0(1+Ƙ(P-P0)).

2. A concrete dam (SG = 2.5) is made in the shape of an isosceles triangle, as shown in
figure. Analyze this geometry to find the range of angles θ for which the hydrostatic force
will tend to tip the dam over at point B. The width into the paper is b.

3. Show that the distance between metacentre and centre of buoyancy is given by
MB = Io/Vsubmerged where Io is the area moment of inertia of the waterline footprint of the
body about its tilt axis and Vsubmerged denotes submerged volume and then determine the
expression of time period of small oscillations of submerged body if it is displaced by a
very small angle. Take radius of gyration about metacentre to be K and derive time period
in terms of GM(distance between centroid and metacentre) and K.

4. The uniform beam in the Figure given below of size L by h by b and with specific weight b,
floats exactly on its diagonal when a heavy uniform sphere is tied to the left corner, as
shown. Show that this can happen only (a) when Ƴb = Ƴ/3 and (b) when the sphere has
size
5. Consider a cylinder of specific gravity S<1 floating vertically in water (S=1). Derive a
formula for the stable values of D/L as a function of S and apply it to the case D/L = 1.2.

6. The 450 V-tube contains water and is open at A and closed at C. What uniform rotation
rate in r/min about axis AB will cause the pressure to be equal at points B and C? For this
condition, at what point in leg BC will the pressure be a minimum?

7. The tank is moving with constant acceleration up a 300 inclined plane, as shown.
Assuming rigid-body motion, compute (a) the value of the acceleration a, (b) whether
the acceleration is up or down, and (c) the gage pressure at point A if the fluid is mercury
at 200C.

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