An engineer is designing a triangular weir for measuring the flow rate of a stream of water that has a discharge of 6 cfm. The weir has an included angle of 45$^{\circ}$ and a coefficient of discharge of 0.6. Find the head on the weir.

Determine the flow of water through the pipe if the difference in pressure between the two ports of the orifice meter is 8 psi. The water has a temperature of 60 degrees F.

The head on a 60$^{\circ}$ triangular weir is 1.8 ft. What is the discharge of water over the weir?

Water flows through a venturi meter that has a 40-cm throat. The venturi meter is in a 70-cm pipe. What deflection will occur on a mercury-water manometer connected between the upstream and throat sections if the discharge is 0.75 m3/s? Assume T=20$^{\circ}C$.

A $15 \mathrm{~cm}$ plate orifice at the end of a $30 \mathrm{~cm}$ pipe is enlarged to $20 \mathrm{~cm}$. With the same pressure drop across the orifice (approximately $50 \mathrm{kPa}$ ), what will be the percentage of increase in discharge?

When a hydrometer having a stem diameter of $0.30\ \mathrm{in}$. is placed in water, the stem protrudes $3.15\ \mathrm{in}$. above the water surface. If the water is replaced with a liquid having a specific gravity of $1.10$, how much of the stem would protrude above the liquid surface? The hydrometer weighs $0.042 \mathrm{lb}$.

An equilateral triangular plate is immersed in water vertically with one edge in the surface. If the length of each side is a, find the total thrust on the plate and the depth of the centre of pressure.

For each of the following pdfs let X1, …, Xn be iid observations. Find a complete sufficient statistic, or show that one does not exist. (a) $f(x | \theta)=\frac{2 x}{\theta^{2}}$, 0 < x < $\theta$, $\theta$ > 0 (b) $f(x | \theta)=\frac{\theta}{(1+x)^{1+\theta}}$ , 0 < x < $\infty$, $\theta$ > 0 (c) $f(x | \theta)=\frac{(\log \theta) \theta^{x}}{\theta-1}$, 0 < x < 1, $\theta$ > 1, (d)

$$f(x | \theta)=\left(\begin{array}{l}{2} \\ {x}\end{array}\right) \theta^{x}(1-\theta)^{2-x}$$

, f(x|$\theta$) = e−(x − $\theta$) exp(−e−(x − $\theta$)), $-\infty<x<\infty,-\infty<\theta<\infty$(e) , x = 0, 1, 2, $0 \leq \theta \leq 1$

A square plate of side 3 m is submerged in water at an incline of $30^{\circ}$ with the horizontal. Its top edge is located at the surface of the water. Calculate the fluid force (in Newtons) on one side of the plate.

A square plate of side a is immersed vertically in water with its upper side horizontal and at a depth d below the surface. Prove that the centre of pressure is at a distance $\frac{a^{2}}{6(a+2 d)}$ below the centre of the square.

A 6-in. orifice is placed in a 10-in. pipe, and a mercury manometer is connected to either side of the orifice. If the flow rate of water (60$^{\circ}F$) through this orifice is 4.5 cfs, what will be the manometer deflection?

Water (p=1000 kg/m3) is accelerated from rest in a horizontal pipe that is 80 m long and 30 cm in diameter. If the acceleration rate (toward the downstream end) is 5 m/s2, what is the pressure at the upstream end if the pressure at the downstream end is 90 kPa gage?

A 3-m-long rectangular weir is to be constructed in a 3-m-wide rectangular channel. (a). The maximum flow in the channel will be 4 m3/s. What should be the height P of the weir to yield a depth of water of 2 m in the channel upstream of the weir?

The head on a 60$^{\circ}$ triangular weir is 25 cm. What is the discharge over the weir in cubic meters per second?