Fluid Mechanics

A vertical cylindrical tank with a 0.4 m diameter circular base holds water, the level of which is a height of 1.3 m from the bottom of the tank. If the tank has a 2.5 cm diameter orifice at its base, calculate the distance the level of water will be from the base of the tank after300 seconds.

\text { Given: } c_{d}=0.5 \text { for the orifice }

\text { Given: } T=\int_{H_{2}}^{H_{1}} \frac{A d h}{C_{d} a \sqrt{2 g h}}

where the symbols have their usual meaning.

A dam is shown in Figure Q2(b). Given the dimensions shown in the diagram, calculate:

(i)The resultant force from the water on the dam per unit width.

(ii)The direction of the resultant force.

A horizontal Venturi meter, pipe diameter of 500 mm and throat diameter of 280 mm, has a discharge coefficient of 0.97. A differential U-tube manometer, using mercury as the manometric fluid, is connected between pressure tappings at the entrance and atthe throat. The Venturi meter is used to measure the flow of water,which fills the leads to the U-tube and is in contact with the mercury.

(i) Calculate the volume flow rate when the difference in the mercury levels is 50 mm. Take densities of water and mercury as 1000 kg/m³ and 13,600 kg/m³ respectively.

\text { Given: } v_{1}=\sqrt{\frac{2 g x\left(\frac{\rho_{m}-\rho_{p}}{\rho_{p}}\right)}{\left(\frac{a_{1}}{a_{2}}\right)^{2}-1}}

\text { Given: } Q=v_{1} \cdot a_{1} \cdot c_{d}

where the symbols have their usual meaning.

In less than 100 words describe the Velocity Pressure and Static Pressure changes as the fluid flows through the meter according to Bernoulli's equation.

A rectangular pontoon floating in salt water of density 1025 kg/m³ is carrying a load. The combined mass of the load and the pontoon is75000 kg. The dimensions of the pontoon are 15 m long, 6 m wide and 2 m high.

Calculate the depth of immersion and freeboard of the pontoon.



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