According to Bernoulli's equation as presented for fluid mechanics, the total head at a point in water under motion is the sum of which three components?
Explanation
Bernoulli's equation is a fundamental principle in fluid mechanics that relates pressure, velocity, and elevation of a moving fluid. The total head is a measure of the total energy of the fluid per unit weight.
Other questions
When applying Bernoulli's equation to the flow of water through a porous soil medium, which component of the total head is typically neglected, and for what reason?
What is the relationship between the discharge velocity (v) and the seepage velocity (vs) in a porous medium with a void ratio (e)?
A soil sample has a discharge velocity (v) of 0.02 cm/sec and a porosity (n) of 0.40. What is the seepage velocity (vs) in the sample?
Which of the following factors does NOT typically affect the hydraulic conductivity of clayey soils?
In a constant-head permeability test, the following values are recorded: volume of water collected (Q) = 350 cm3, length of the specimen (L) = 30 cm, area of the specimen (A) = 177 cm2, constant-head difference (h) = 50 cm, and duration of the test (t) = 5 minutes. What is the hydraulic conductivity (k) in cm/sec?
For a falling-head permeability test, the following values are given: length of specimen (L) = 8 in, area of soil specimen (A) = 1.6 in^2, area of standpipe (a) = 0.06 in^2, initial head difference (h1) = 20 in, and final head difference (h2) = 12 in. The test duration (t) was 180 sec. What is the hydraulic conductivity (k) of the soil in in/sec?
A laboratory test finds the hydraulic conductivity of a soil at 15 degrees Celsius to be 0.010 cm/sec. Given that the ratio of viscosities (ηT°C/η20°C) for T=15 C is 1.135, what is the hydraulic conductivity corrected to the standard temperature of 20 degrees Celsius?
According to the Kozeny-Carman equation, how is hydraulic conductivity (k) related to the void ratio (e) of the soil?
The hydraulic conductivity of a sand at a void ratio of 0.5 is 0.02 cm/sec. Using the relationship derived from the Kozeny-Carman equation (k is proportional to e^3/(1+e)), estimate its hydraulic conductivity at a void ratio of 0.65.
For a normally consolidated clay soil, laboratory tests show a hydraulic conductivity of 0.302 x 10^-7 cm/sec at a void ratio of 1.1, and 0.120 x 10^-7 cm/sec at a void ratio of 0.9. Using the relationship k = C * (e^n / (1+e)), what is the value of the exponent n?
For flow parallel to the layers in a stratified soil deposit (horizontal flow), how is the equivalent hydraulic conductivity, kH(eq), calculated?
For flow perpendicular to the layers in a stratified soil deposit (vertical flow), how is the equivalent hydraulic conductivity, kV(eq), calculated?
A layered soil consists of three layers with properties: H1 = 2 m, k1 = 10^-4 cm/sec; H2 = 3 m, k2 = 3.2 x 10^-2 cm/sec; H3 = 4 m, k3 = 4.1 x 10^-5 cm/sec. Assuming the horizontal and vertical conductivities are the same for each layer, what is the ratio of equivalent horizontal hydraulic conductivity to equivalent vertical hydraulic conductivity (kH(eq)/kV(eq))?
Three layers of soil are in a tube 100 mm by 100 mm in cross section. A constant-head difference of 300 mm is maintained across the total sample length of 450 mm. The layers are each 150 mm thick with hydraulic conductivities of k_A = 10^-2 cm/sec, k_B = 3 x 10^-3 cm/sec, and k_C = 4.9 x 10^-4 cm/sec. What is the rate of water supply (flow rate) in cm3/hr?
For fairly uniform sand, what empirical relationship for hydraulic conductivity (k) in cm/sec did Hazen (1930) propose?
Which statement accurately describes the reliability of Hazen's empirical relationship for hydraulic conductivity?
Chapuis (2004) proposed an empirical relationship for hydraulic conductivity (k) that is valid for natural, uniform sand and gravel in what range of k values?
For a pumping test from a well in an unconfined aquifer underlain by an impermeable stratum, what is the formula for calculating the hydraulic conductivity (k)?
What is the primary difference in the flow condition between a confined aquifer and an unconfined aquifer that leads to different formulas for hydraulic conductivity from a pumping test?
In a stratified soil with horizontal layers, the equivalent horizontal hydraulic conductivity (kH(eq)) is generally...
What does Taylor (1948) propose as the relationship between the logarithm of hydraulic conductivity (k) and the void ratio (e) for some soils?
For a pumping test in a confined aquifer of thickness H=10 m, the steady-state pump discharge is q=0.02 m3/sec. The piezometric heads in two observation wells at r1=50 m and r2=20 m are h1=8 m and h2=6 m, respectively. Calculate the hydraulic conductivity (k) in m/sec.
What is the primary purpose of the laboratory falling-head permeability test?
In the context of flow through saturated soils, which of these statements about Darcy's Law is correct?
What type of flow conditions may exist in fractured rock, stones, and very coarse sands, where Darcy's Law may not be valid?
A stratified soil deposit consists of two horizontal layers. Layer 1 has thickness H1 = 4m and k1 = 2x10^-4 m/s. Layer 2 has thickness H2 = 6m and k2 = 5x10^-5 m/s. What is the equivalent horizontal hydraulic conductivity, kH(eq)?
A stratified soil deposit consists of two horizontal layers. Layer 1 has thickness H1 = 4m and k1 = 2x10^-4 m/s. Layer 2 has thickness H2 = 6m and k2 = 5x10^-5 m/s. What is the equivalent vertical hydraulic conductivity, kV(eq)?
According to Table 7.3, what is a typical range for the ratio of horizontal to vertical hydraulic conductivity (kH/kV) for Varved clay?
What is the physical meaning of the term 'absolute permeability', K?
What is the typical value for the hydraulic conductivity of Clay, in cm/sec, according to Table 7.1?
According to the laboratory test results for a permeable soil layer underlain by an impervious layer as shown in Example 7.4, if the hydraulic conductivity (k) is 5.3 x 10^-5 m/sec, H = 3 m, and the slope angle (α) is 8 degrees, what is the rate of seepage (q) in m3/hr/m width?
For the flow through a permeable layer shown in Example 7.5, given H = 8 m, H1 = 3 m, h = 4 m, L = 50 m, α = 8 degrees, and k = 0.08 cm/sec, what is the flow rate (q) in m3/sec/m length?
For which of the following materials is the Chapuis (2004) empirical relationship for hydraulic conductivity NOT considered valid?
What does the Amer and Awad (1974) relationship for hydraulic conductivity in granular soil incorporate that Hazen's formula does not?
For a sandy soil with D10 = 0.2 mm, a uniformity coefficient Cu = 2.0, and a void ratio e = 0.7, what is the estimated hydraulic conductivity (k) in cm/sec at 20 C using the simplified Amer and Awad formula (Eq. 7.34)?
A grain-size distribution for a sand gives D10 = 0.09 mm. The void ratio is 0.6. Estimate the hydraulic conductivity (k) in cm/sec using the Chapuis formula (Eq. 7.32).
For compacted fine-grained soils, what does Table 7.3 indicate about the typical ratio of horizontal to vertical permeability (kH/kV)?
According to the summary of factors affecting laboratory determination of hydraulic conductivity, which of the following is NOT listed as a potential issue?
In a Boutwell permeameter test, after the initial test (calculating k1), the hole is deepened by augering and a second falling-head test is conducted. What is the primary purpose of this two-stage process?
What is the definition of a piezometric level at a point in soil?
According to Figure 7.2, showing the nature of variation of discharge velocity (v) with hydraulic gradient (i), what happens in Zone III?
What physical feature of a soil deposit is described as being 'rhythmically layered sediment of coarse and fine minerals' resulting from 'annual seasonal fluctuation'?
A grain-size distribution curve for a sand is provided. D60 is 0.16 mm and D10 is 0.09 mm. What is the uniformity coefficient (Cu) for this sand?
The relationship between log k and log e for a sodium clay mineral is plotted in Figure 7.12. What does this plot suggest about the relationship?
What are the two standard laboratory tests used to determine the hydraulic conductivity of soil as described in Section 7.4?
In a permeability test on a sand with a void ratio of 0.58, the hydraulic conductivity (k) was found to be 0.0118 cm/sec. The head difference was 500 mm and the length of the sample was 300 mm. What was the seepage velocity?
What is the primary characteristic of flow that distinguishes Zone I from Zone II and Zone III in the velocity vs. hydraulic gradient plot (Figure 7.2)?
What is the equation for the hydraulic gradient, i, in its nondimensional form?
A pumping test is conducted in an unconfined aquifer. The pump discharges at a steady rate of 0.01 m3/sec. The water levels in two observation wells are h1=12 m at r1=60 m and h2=10 m at r2=30 m. What is the hydraulic conductivity (k) of the soil in m/sec?