Name: Angle of Contact
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: What is the contact angle? Which factor does the contact angle depend on? Why does the contact angle for the same liquid on different surfaces differ? Let's...

Question

(i) Distinguish between streamline flow and turbulent flow.

(ii) Show that Bernoulli's equation is same as the equation due to Pascal's law in presence of gravity, if a liquid or a gas is at rest.

Accepted Answer

(i) Streamline Flow

1. In a streamline flow each following (oncoming) particle follows exactly the same path as that of its predecessor.

2. Flow is steady and different layers of liquid move parallel to each other.

3. Reynolds number is usually less than $< 1000$ for a streamline flow.

4. Fluid velocity remains constant at any point of a streamline, but it may be different at different points of the same streamline.

5. It occurs at low speeds.

6. A streamline motion can be represented with help of a bundle of streamlines.

Turbulent Flow:

1. The haphazard and zig-zig flow of fluid particles is called turbulent flow.

2. It is accompanied by random irregular local circular currents called eddies.

3. It occurs at high flow speeds.

4. Mostly Reynolds number $> 2000$ for the flow to be turbulent.

5. It leads to dissipation of kinetic energy as heat.

6. Turbulent motion increases the rate of transfer of mass, momentum and energy.

(ii) According to Bernoulli's principle, $P_{1} + \frac{1}{2} ρ v_{1}^{2} + ρ g h_{1} = P_{2} + \frac{1}{2} ρ v_{2}^{2} + ρ g h_{2}$ .

If the fluid is at rest,

$\Rightarrow v_{1} = v_{2} = 0$

Then, $P_{1} + ρ g h_{1} = P_{2} + ρ g h_{2}$

$\Rightarrow P_{1} - P_{2} = ρ g (h_{2} - h_{1})$

Which is a mathematical form of Pascal's law, i.e. at $h_{1} = h_{2}, P_{1} - P_{2} = 0$

(i) Distinguish between streamline flow and turbulent flow.

(ii) Show that Bernoulli's equation is same as the equation due to Pascal's law in presence of gravity, if a liquid or a gas is at rest.

Important Questions on Mechanical Properties of Fluids

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