# NCERT Class 11 Physics Solutions: Chapter 10 – Mechanical Properties of Fluids-Part 6

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Question 10.12:

Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain.

Explanation:

It does not matter if one uses gauge pressure instead of absolute pressure while applying Bernoulli’s equation. The two points where Bernoulli’s equation is applied should have significantly different atmospheric pressures.

Question 10.13:

Glycerin flows steadily through a horizontal tube of length and radius If the amount of glycerin collected per second at one end is, what is the pressure difference between the two ends of the tube? (Density of glycerin and viscosity of glycerin [You may also like to check if the assumption of laminar flow in the tube is correct].

Explanation:

Length of the horizontal tube,

Diameter of the tube,

Glycerin is flowing at a rate of

Density of glycerin,

Viscosity of glycerin,

Volume of glycerin flowing per sec:

According to Poi Seville’s formula, we have the relation for the rate of flow:

Where, is the pressure difference between the two ends of the tube.

Reynolds’ number is given by the relation:

Reynolds’ number is about. Hence, the flow is laminar.

Question 10.14:

In a test experiment on a model aero plane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are respectively. What is the lift on the wing if its area is ? Take the density of air to be

Speed of wind on the upper surface of the wing,

Speed of wind on the lower surface of the wing,

Area of the wing,

Density of air,

According to Bernoulli’s theorem, we have the relation:

Where,

Pressure on the upper surface of the wing

Pressure on the lower surface of the wing

The pressure difference between the upper and lower surfaces of the wing provides lift to the aero plane.

Lift on the wing

Therefore, the lift on the wing of the aero plane is