Question

Fluid Mechanics

Use area integration to calculate the centre of mass of a triangle with vertices at (0, 0),(0, 1), (2, 0).(a)(i)[10 marks]

Hence find the centre of mass of the object(ii)shown in the diagram below (you may assume that the centre of mass of a rectangle is located at the midpoints of both sides). You may use the

\text { result } \overline{\mathbf{r}}=\frac{1}{S} \sum_{i=1}^{n} S_{i} \overline{\mathbf{r}}_{i} \text { . }

Find the mass of the unit cube occupying the region

0 \leq x \leq 1,0 \leq y \leq 1,0 \leq z \leq 1, \text { With density } \rho(x, y, z)=x^{2}+2 x y^{2}+z

Verified

### Question 45484

Fluid Mechanics

Water in the Belle Fourche Reservoir in Western South Dakotais transported to the water storage reservoir for the town of-Buffalo through a series of three pipes, all with friction factors of 0.02. The first pipe is 500 meters long with a diameter of 0.4meters; the second pipe is 600 meters long with a diameter of0.3 meters; and the third pipe is 500 meters long with a diameter of 0.2 meters. The water surface elevation of the Belle FourcheReservoir is 30 meters higher than the town's storage reservoir.Since the current piping is almost 60 years old, the town of Buffalo has decided to replace the piping system with a single pipe of constant diameter. You have been chosen to calculate the equivalent diameter for the single pipe design and determine the flow rate that will occur. Go to work.

### Question 44899

Fluid Mechanics

Transmission lines

### Question 44896

Fluid Mechanics

A boat has a volume of 40.0 m³ and a mass of 2.00 tons. What load will push 75.0% of its volume into water? Each Metric ton is 1000 kg.

### Question 44895

Fluid Mechanics

A tank has a height of 800 mm and a length of 500 mm. The tank contains a liquid of RD 0.9.Determine:
a. The magnitude of the force on the side of the tank per meter width and its position relative to the base of the tank
b. The force on the base per meter width of tank.

### Question 44894

Fluid Mechanics

A closed tank contains three different fluids with a vapor space above the oil, as shown in the figure below. Pressure gauge 1 reads the gauge pressure of the vapor space (P1) and pressure gauge 2 reads the pressure at the bottom of the tank (P2). When P1 = 25 kPa, determine:
a. Height of glycerine (h) in the tank if P2 = 95.66 kPa
. P2 reading if glycerine is replaced with water

### Question 44805

Fluid Mechanics

Water flows into cylindrical tank through inlet A and D at rate of 20 ft/s and 5 ft/s respectively. If waterleaves through outlet B and C at rate of 3 ft/s and 10 ft/s respectively.
(A) Derive the continuity equation
\text { Know that } D_{A}=2.5 \text { in, } D_{D}=2 \text { in } D_{B}=3 \text { in and } D_{C}=3.5 \text { in. }
(B) Calculate the change of high h?

### Question 44804

Fluid Mechanics

An object which has cubic shape is been floating on the water surface see the diagram below. If the object density is less than water, density find the ratio X/L?

### Question 44803

Fluid Mechanics

A force of 15.83 kN is exerted on a piston B (diameter = 250 mm) which fits into a cylinder see the diagram below. How much force is need on piston C to start displacing piston B and Mercury on piston B?

### Question 44802

Fluid Mechanics

Given the diagram below if the pressure gauge reads 6.1 psig find Y and X in ft. Given that
\mathrm{SG}_{\mathrm{Aloohal}}=0.9, \mathrm{SG}_{\mathrm{Hg}}=13.6, \text { Alcohol vapor } P=1.7 \mathrm{psig}, Z=4 \mathrm{ft} \text { and } \mathrm{Y}_{\mathrm{H} 2 \mathrm{o}}=62.4 \mathrm{\textrm {lb }} / \mathrm{ft}^{3}

### Question 44801

Fluid Mechanics

Given the diagram below, calculate the pressure at A, B, C.
\text { Given that } \mathrm{Y} \text { н2о }=9.79 \mathrm{kN} / \mathrm{m}